Direct Measurement of Competing Quantum Effects in Kinetic Energy of - PowerPoint PPT Presentation

VI electron Volt Neutron Spettroscopy: Frontiers and Horizons Direct Measurement of Competing Quantum Effects in Kinetic Energy of Heavy Water upon Melting Giovanni Romanelli, Michele Ceriotti, David Manoulopulos, Claudia Pantalei, Roberto Senesi, Carla Andreani January 20, 2014 University of Roma Tor Vergata Nast Center Giovanni Romanelli VI eVS Workshop January 20, 2014 1 / 14

Table of Contents 1 Introduction Quantum Mechanics and Nuclear Motion Kinetic Energy and macroscopic properties 2 The Experiment Vesuvio can see the Momentum Distribution Experimental Data What momentum Distribution? Correction of Final State Effects 3 Results Fitted signals Measure of Competing Quantum Effects The Quantum Nature of Oxygen Simple comparison 4 Conclusions Giovanni Romanelli VI eVS Workshop January 20, 2014 2 / 14

Quantum Mechanics and Nuclear Motion The structure and dynamics of Water are directly influenced by Quantum Mechanics, even in Nuclear Motion Nuclear Quantum Effects Zero-point Energy Tunneling Large deviations from MB Isotope effects Light and Heavy Water 4 K in melting point 1 K in boiling point Big contributions, but partial cancellation in the intra end intermolecular components of the hydrogen Bonding. Giovanni Romanelli VI eVS Workshop January 20, 2014 3 / 14

Kinetic Energy and macroscopic properties The change of many thermodynamic properties upon isotopic substitution can be related to the changes in the Kinetic Energy. It is possible to relate the change in the Kinetic Energy of the D atom in the Melting of Heavy Water to macroscopic properties ∆ fus S ( m H ) � [ T fus ( m H ) − T fus ( m D )] . ∆ fus E K ( m D , T fus ( m D )) ≈ �� 2 m D /m H − 1 We have a simple prediction: ∆ fus E K ( m D , T fus ( m D )) = − 0 . 5 meV Giovanni Romanelli VI eVS Workshop January 20, 2014 4 / 14

Vesuvio can see the Momentum Distribution High Energy and High momentum transfer → Impulse Approximation ω − � q 2 � � � q � y = m m S IA ( q , ω ) = J IA ( y , ˆ q ) = n ( p ) δ ( y − p · ˆ q ) d p � q 2m Giovanni Romanelli VI eVS Workshop January 20, 2014 5 / 14

Experimental Data t.o.f. data collected both in forward and backward scattering θ =62 ◦ θ =136 ◦ C ( t ) µ µ 5 mm thickness D 2 O upon Melting simulated multiple scattering 274 K (solid phase) Cu can and O signals 280 K (liquid phase) separated Giovanni Romanelli VI eVS Workshop January 20, 2014 6 / 14

What momentum Distribution? Sample has no angular polarization.Only p = | p | dependence can be measured. � 3 / 2 − mv 2 � m � � n MB ( p ) = exp (1) 2 πk B T 2 k B T Maxwell Boltzman distribution cannot capture anysotropy or anharmocity of the sample. It will be taken as a comparison. � 3 / 2 − mv 2 − mv 2 � � � � � � m 1 c n ( − 1) n L n GH ( p ) = exp 2 (2) n 2 πk B T 2 k B T 2 k B T n Laguerre polynomials can adapt a MB distribution to experimental data, but the result is not simply interpreted. � � � − p 2 p 2 − p 2 1 � y x z n ( p ) = exp (3) √ − 2 σ 2 2 σ 2 2 σ 2 8 π 3 σ x σ y σ z Ω x y z A multi varied Gaussian can recognize the anisotropy of the system, and lead to a simple interpretation. Giovanni Romanelli VI eVS Workshop January 20, 2014 7 / 14

Correction of Final State Effects Since the q value is not infinite, corrections must be taken into account. F ( y, q ) = [ J IA ( y ) + ∆ J ( y, q )] ⋆ R ( y, q ) The correction si choosen as an addictive term (Sears, Phys Rev B 30 44 1984) ∆ J ( y, q ) = − A 3 ( q ) ∂ 3 ∂y 3 J IA ( y ) The resolution function R ( y, q ) is simulated by well tested routines. Experimental data are composed on a even IA signal and an odd FSE correction Giovanni Romanelli VI eVS Workshop January 20, 2014 8 / 14

Fitted Signals F � y , q � � � � 0.06 38 � D Σ Α 66 � � Σ � 0.04 EXP � 20 0 20 R � y � 0.02 0 � 20 0 20 0.06 O 132 � J. Phys. Chem. Lett., 2013, 4 (19), pp 3251–3256 156 � 0.04 � 50 0 Results on D 2 O: 0.02 first time Oxygen is isolated 0 Anisotropy of O and D y � � � 1 � � 50 0 recognized Giovanni Romanelli VI eVS Workshop January 20, 2014 9 / 14

Measure of Competing Quantum Effects Deuterium Oxygen Qualitative agreement Exp - Sim First time Oxygen signal isolated CQE measured: upon melting Qualitative agreement Exp - Sim ◮ x-component decreases � E K � greater of 50% respect to ◮ y-component increases � E COM � Giovanni Romanelli VI eVS Workshop January 20, 2014 10 / 14

The Quantum Nature of Oxygen The center of mass energy (from simulation) at T = 280 K is � E COM � = 39 . 5 meV > 3 2 k B T = 36 . 2 meV About 3% more energy with respect to MB → Quantum effects on inter-molecolar Dynamics Oxygen Dynamics is highly quantistic: its kinetic energy is in eccess of 50% with respect to COM. anysotropy of its momentum distribution have been revealed. Vesuvio can access Momentum Distribution, Kinetic Energy and Nuclear Quantum Effects of hevier masses! Giovanni Romanelli VI eVS Workshop January 20, 2014 11 / 14

Simple comparison.. What if we calculate the � E K � z from vibrational (Raman) frequencies? � ω str coth � ω str 1 � E K � z = 2 S str 2 k B T + S tra 2 k B T 4 Stretching frequencies Kinetic fractions � ω str,solid = 285 meV S str = 0 . 46 � ω str,liquid = 301 meV S tra = 0 . 10 Overestimation of both the components and the melting energy: � E K � z ( liquid, 280 K) = 68 . 6 meV � E K � z ( solid, 274 K) = 65 . 1 meV ∆ fus � E K � z = 3 . 5 meV (TAG/MSD: 1.7/2.2 meV) Giovanni Romanelli VI eVS Workshop January 20, 2014 12 / 14

Conclusions Quantum nature of Oxygen has been revealed Competing Quantum Effects have been recognized in the Melting Anharmonicity effects can be recognized Same experiment have been done on liqht water Giovanni Romanelli VI eVS Workshop January 20, 2014 13 / 14

Thank you for your attention! Giovanni Romanelli VI eVS Workshop January 20, 2014 14 / 14