Inelastic Scattering: Neutrons vs X-rays

Inelastic Scattering:Neutrons vs X-rays Stephen Shapiro Condensed 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

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 Neutrons X-rays

+’s -’s Low energy Rad. Source Bulk penetration Weak source Mag. Moment Weak Interaction Isotope sub. Need lge. sample Put int. on abs. basis Resolution well known Versatility of Inst. Many instruments +’s -’s Very intense Interact with e- Small beam size Little penetration Large ki Need high res. Weak mag. Int. Few instruments InelasticNeutrons X-rays

Similarities Measure the same thing: Fluctuation Dissipation Theorem Energy Conservation: Momentum Conservation:

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 Monochromator ki, Ei Source 2M Sample Analyzer 2S kf, Ef 2A

Inelastic Instruments Consider phonons: 1-100 meV 1 meV = 8.07 cm-1= 0.24 THz X-rays: Ei~10 keV E/Ei ~ 10-7 Neutrons: Ei~10 meV E/Ei ~ 10-1 How to achieve?? M,A ~ 45 M,A ~ 90

Neutron X-Ray BT7 - NIST ID16 - ESRF

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 APS 2 Europe ESRF 2 ASIA SPRING-8 1 Number of Inelastic Instruments with meV resolutions

Experiments • Phonon dispersion curve anomalies • Phase transitions • Phonon linewidths

Electron Phonon Coupling Nb: Sample size: 5 cm3 B. M. Powell, P. Martel, A.D.B. Woods, Phys. Rev 171, 727 (1968)

 - FCC Pu-Ga • ESRF ID28 • Sample Size: • Large Grain • [30 x 60] x10 • m3 J. Wong et al., Phys Rev. B72, 064115 (2005)

Structural Phase Transitions AuxZn1-x Martensite Transition 65K SrTiO3 x=?? x=.5

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 Habicht et al. PRB 69, 104301 (2004)

Linewidth Measurements:Neutron Spin Echo TRISP Instrument @ FRMII, Munich Aynajian, Keller, Boeri, Shapiro, Habicht, Keimerr Science, to be published (2008)

Phonons in Thermoelectrics AgPbmSbTe2+m AgSbTe2 - PbTem LAST - m • Power generating devices • Figure of merit • Reduce  • Reduce phonon lifetime • Measure by linewidths in single crystals m=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

Inelastic Scattering: Neutrons vs X-rays