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

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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.

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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 ∆fusEK(mD, Tfus(mD)) ≈ ∆fusS(mH) 2

• mD/mH − 1

[Tfus(mH) − Tfus(mD)] .

We have a simple prediction:

∆fusEK(mD, Tfus(mD)) = −0.5 meV

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Vesuvio can see the Momentum Distribution

High Energy and High momentum transfer → Impulse Approximation q m SIA(q, ω) = JIA(y, ˆ q) =

• n(p)δ (y − p · ˆ

q) dp y = m q

• ω − q2

2m

• Giovanni Romanelli

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Experimental Data

t.o.f. data collected both in forward and backward scattering

C(t) µ

θ=62◦

µ

θ=136◦

D2O upon Melting

274 K (solid phase) 280 K (liquid phase) 5 mm thickness simulated multiple scattering Cu can and O signals separated

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What momentum Distribution?

Sample has no angular polarization.Only p = |p| dependence can be measured.

nMB(p) =

• m

2πkBT 3/2 exp

• − mv2

2kBT

• (1)

Maxwell Boltzman distribution cannot capture anysotropy or anharmocity of the sample. It will be taken as a comparison. nGH(p) =

• m

2πkBT 3/2 exp

• − mv2

2kBT

n

cn(−1)nL

1 2

n

• − mv2

2kBT

• (2)

Laguerre polynomials can adapt a MB distribution to experimental data, but the result is not simply interpreted. n(p) =

• 1

√ 8π3σxσyσz exp

• − p2

x

2σ2

x

− p2

y

2σ2

y

− p2

z

2σ2

z Ω

(3) A multi varied Gaussian can recognize the anisotropy of the system, and lead to a simple interpretation.

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Correction of Final State Effects

Since the q value is not infinite, corrections must be taken into account. F(y, q) = [JIA(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) = −A3(q) ∂3 ∂y3 JIA(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

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Fitted Signals

50 0.02 0.04 0.06 Σ ΣΑ Ry EXP 20 20 0.02 0.04 0.06

66 38 20 20 156 132 50

y 1 Fy,q D O

• J. Phys. Chem. Lett., 2013, 4 (19),

pp 3251–3256

Results on D2O:

first time Oxygen is isolated Anisotropy of O and D recognized

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Measure of Competing Quantum Effects

Deuterium

Qualitative agreement Exp - Sim CQE measured: upon melting

◮ x-component decreases ◮ y-component increases

Oxygen

First time Oxygen signal isolated Qualitative agreement Exp - Sim EK greater of 50% respect to ECOM

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The Quantum Nature of Oxygen

The center of mass energy (from simulation) at T = 280 K is ECOM = 39.5 meV > 3 2kBT = 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!

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Simple comparison..

What if we calculate the EKz from vibrational (Raman) frequencies? EKz = 2Sstr ωstr 4 coth ωstr 2kBT + Stra 1 2kBT

Stretching frequencies

ωstr,solid = 285 meV ωstr,liquid = 301 meV

Kinetic fractions

Sstr = 0.46 Stra = 0.10 Overestimation of both the components and the melting energy: EKz( liquid, 280 K) = 68.6 meV EKz( solid, 274 K) = 65.1 meV ∆fusEKz = 3.5 meV (TAG/MSD: 1.7/2.2 meV)

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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

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Thank you for your attention!

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