Transcript ISIS Poster Template

Neutron scattering studies of quantum fluids: hydrogen
www.ifac.cnr.it
U.
(a)
Bafile ,
M.
(a)
Celli ,
D.
(a)
Colognesi ,
www.infm.it
F.
(b)
Formisano ,
www.ifac.cnr.it/idrogeno
E.
(c)
Guarini ,
R.
(c,d)
Magli ,
M.
(a)
Zoppi
[email protected]
(a) Istituto di Fisica Applicata ‘Nello Carrara’, Consiglio Nazionale delle Ricerche, Italy
(b) Istituto Nazionale per la Fisica della Materia, Operative Group in Grenoble, France
(c) Istituto Nazionale per la Fisica della Materia, Unità di Firenze, Italy
(d) Dipartimento di Chimica, Biochimica e Biotecnologie per la Medicina, Università di Milano, Italy
The microscopic structure of liquid
hydrogen
is a still open problem [1], because x-ray and neutron
spectroscopy are of difficult application to such a system, a
much harder case than deuterium, already solved a decade ago
[2].
Experimental data
The diffraction pattern of saturated liquid parahydrogen was
measured with the D4C diffractometer of ILL, Grenoble
Sample data: temperature
T = 17.1 K
pressure
p = 29.9 bar
molecular number density n = 22.95 nm-3
concentration of para species > 0.9995
(by using a catalyst in the sample container)
References
Models and calculations
Results
The single-molecule scattering can be exactly calculated by modelling the
hydrogen molecules as freely rotating harmonic oscillators [3], taking into
account the density and temperature dependence of the centre-of-mass kinetic
energy of a quantum system [4]. Wavelength-dependent detector efficiency,
attenuation, and the influence of the finite size of sample, container, and
detectors, can all be taken into proper account.
The determination of the static structure of liquid
hydrogen is demonstrated to be a feasible,
though difficult, task. Reliable data can be
obtained by the joint use of neutron diffraction
and quantum-mechanical simulation [5].
[1] F.J. Bermejo, K. Kinugawa, C. Cabrillo, S.M.
Bennington, B. Fåk, M.T. Fernández-Díaz, P.
Verkerk, J. Dawidowski, and R. Fernández-Perea,
Phys. Rev. Lett. 84, 5359 (1998); A. Cunsolo, G.
Pratesi, D. Colognesi. R. Verbeni, M. Sampoli, F.
Sette, G. Ruocco, R. Senesi, M.H. Krisch, and M.
Nardone, J. Low Temp. Phys. 129, 117 (2002).
[2] M. Zoppi, U. Bafile, R. Magli, and A.K. Soper,
Phys. Rev E 48, 1000 (1993); E. Guarini, F. Barocchi,
R. Magli, U. Bafile, and M.-C. Bellissent-Funel, J.
Phys.: Condens. Matter 7, 5777 (1995); M. Zoppi, U.
Bafile, E. Guarini, F. Barocchi, R. Magli, and M.
Neumann, Phys. Rev. Lett. 75, 1779 (1995).
-1
The microscopic dynamics of
condensed hydrogen
2.5
109
[3] J.A. Young and J.U. Koppel, Phys. Rev A 135, 603
(1964); M. Zoppi, Physica B 183, 235 (1993); E.
Guarini, J. Phys.: Condens. Matter 15, R775 (2003).
J=0 -> 1
[4] M. Celli, D. Colognesi. and M. Zoppi, Eur. Phys. J.
B 14, 239 (2000).
2.0
Intensity (a.u.)
The physical problem is the study of the single particle
dynamics in condensed quantum systems. From the
high-energy, high-wavevector region of hydrogen
spectrum (E > 100 meV, Q > 80 nm-1) one can obtain
information on the momentum distribution and the
density-dependent mean kinetic energy <Ek> of the
particle. From the low-energy region one can extract
information on the Fourier transform of the velocity
autocorrelation function (liquid) and on the phonon
density of states (solid).
81
Q (nm )
131 149 166 180 194 207 218
[5] M. Zoppi, U. Bafile, M. Celli, G.J. Cuello, F.
Formisano, E. Guarini, R. Magli, and M. Neumann, J.
Phys.: Condens. Matter 15, S107 (2003); M. Zoppi,
M. Neumann, and M. Celli, Phys. Rev B 65, 092204
(2002).
Experimental spectrum
1.5
J=0 -> 3
1.0
J=0 -> 5
J=0 -> 7
[6] M. Celli, D. Colognesi, M. Zoppi, Eur. Phys. J. B.
14, 239 (2000).
0.5
[7] M. Zoppi, D. Colognesi, M. Celli, Eur. Phys. J. B.
23, 171 (2001).
0.0
0
200
400
600
800
[8] M. Zoppi, D. Colognesi, M. Celli, Europhys. Lett.
53, 34 (2001); M. Celli, D. Colognesi, M. Zoppi, Phys.
Rev. E 66, 021202 (2002)
1000
E ( meV)
Experimental data
Experiment
Simulation
90
solid
80
liquid
70
60
Models and calculations
50
0.025
0.020
0.015
0.010
Experiment
Simulation
0.005
0.000
20
22
24
26
28
30
32
-3
The scattering cross section is obtained in the
hypothesis of the translational motion of the molecular
center of mass uncoupled from the molecular internal
motion. The internal dynamics is described by means
of a quantum free rotating harmonic oscillator model
[3]. The self dynamics of the molecular center of mass
requires different models according to the energy and
wavevector range investigated.
Liquid parahydrogen
-1
100
Kinetic Energy ( K)
Sample data:- pH2 at low pressure and at seven
temperatures (12 < T/K < 21) [6] and - along the
isotherm T = 19.3 K, crossing the melting transition,
with pressure 17 bar to 636 bar [7].
0.030
Translational Kinetic Energy of pH2 at T= 19.3 K
110
Scattering cross section ( meV )
The incoherent scattering function of liquid and solid
para-hydrogen was measured using inelastic neutron
scattering by the TOSCA spectrometer at the pulsed
neutron source ISIS (UK).
density ( nm )
0
20
40
60
80
(meV)
High-Q region results
Low-Q region results
As expected, a strong density dependence of the center of mass
mean kinetic energy, characteristic of a quantum systems, is
evident and the comparison with the simulation is excellent [6,7].
The agreement between the experimental self dynamic
structure factor of the molecular center of mass with a
quantum simulation is impressive [8].