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

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

Inelastic NeutronsX-rays +’s-’s Low energyRad. Source Bulk penetrationWeak source Mag. MomentWeak 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 k i Need high res. Weak mag. Int. Few instruments

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 Source Monochromator 2M2M 2S2S 2A2A Sample Analyzer k i, E i k f, E f

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

ID16 - ESRF BT7 - NIST NeutronX-Ray

Number of Inelastic Instruments with meV resolutions  Neutrons US - NIST5 - HFIR 4 - SNS 6 - LANSCE 1 EUROPE - ILL16 - FRMII5 - LLB7 - PSI 4 - ISIS9 ASIA - …….  X-rays US - APS2 Europe - ESRF2 ASIA - SPRING-81

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 cm 3

 - FCC Pu-Ga J. Wong et al., Phys Rev. B72, (2005) ESRF ID28 Sample Size: Large Grain [30 x 60] x10  m 3

Structural Phase Transitions SrTiO 3 Au x Zn 1-x Martensite Transition 65K x=.5 x=??

High T c Superconductors IXS: Fukuda et al. PR B 71, , (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, (2004)

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

Phonons in Thermoelectrics  Power generating devices  Figure of merit  Reduce  Reduce phonon lifetime Measure by linewidths in single crystals AgPb m SbTe 2+m AgSbTe 2 - PbTe m LAST - m 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