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Investigation of collective excitations in liquid neon by means of neutron scattering at small scattering vectors
Volume 45A, number 6
5 November 1973
PHYSICS LETTERS
INVESTIGATION
OF COLLECTIVE
BY MEANS OF NEUTRON
EXCITATIONS
SCATTERING
AT SMALL
IN LIQUID NEON SCATTERING
VECTORS
H.G. BELL, A. KOLLMAR, B. ALEFELD and T. SPRINGER Institu t fir Festkiirperforschung
der Kernforschungsanlage,
Jiilich, 517 Jiilich, Federal Republic of Germany
Received 4 September 1973 Coherent neutron scattering on neon has been investigated above the coexistence curve for scattering vectors Q between 0.06 and 0.5 A-’ with an energy resolution of 6 X lO_’ eV. In addition to a central line, side peaks were ob served in a region of 0.06 <, Q 5 0.14 B;‘. The peaks are interpreted in terms of propagating collective excitations.
In a simple liquid one expects the existence of thermally excited collective density fluctuations which have the character of propagating waves. These modes are responsible for “Brillouin peaks” in the spectrum of scattered radiation which appear at energy transfers hw=+fivQ,
(1)
Q = k. - k, is the scattering vector, v is the velocity of propagation of these modes. In addition one expects a central line due to non-propagating fluctuations. In the case of light scattering where hydrodynamical theory holds, v is determined by the adiabatic sound velocity [ 11. On the other hand, neutron scattering allows the investigation of collective fluctuations with rather short wavelengths (N lO*A) and high frequencies & lOI sec’l) so that one can go far beyond the hydrodynamic region (cf. [2-41). By neutron spectroscopy sharp “Brillouin peaks” have been observed only on superfluid helium [5]. A weak indication of such peaks was reported for liquid Pb [6]. A number of neutron experiments has been carried out at rather large Q-values @Y0.5 A-l) so that the atomistic structure of the liquid comes into play, and eq. (1) is no longer valid. Also in this region indications of propagating,excitations have been reported, namely on various liquid metals [3] and, very recently, in a rather well defined manner on liquid parahydrogen [7]. We were able to perform neutron scattering experiments on neon at rather small scatteringvectors, namely 0.06 < Q < 0.14 A-l with a Q-resolution of 0.02 A-1 and an energy width (tivhm) of 6 X 10-S eV. These experiments are in the gap between neutron scattering experiments at large Q-values (> 0.8 A--‘) [4] where no indication of collective propagating modes has been
observed, and Brillouin scattering experiments with light [8]. Constant-Q runs were carried out at the high resolution triple axis spectrometer with double-monochromator; it is situated at one of the neutron guides on the FRJZcold source. The sample (5 cm height, 3 cm diam.) had a transmission of about 94%. The choice of a low incident energy (2.29 X lob3 eV) avoids scattering due to the first peak of the structure factor. The experimental conditions of the neon were: p = 0.48 g cm-3 = ~~withT=70K;60K;50K;45K; p = 0.75 g cm-3 with 46 K; 50 K; 55 K, and p = 0.98 g cmM3 with 40 K.
ENERGY TRANSFER
hw
lmdl
Fig. 1. Solid lines: Non-corrected neutron spectra on neon for p = pc = 0.48 g cm3 and T = 70 K, at different scattering vectors Q. Dashed line: Spectrum corrected for background and analyzer efficiency. A = energy resolution (fwhm).
479
Volume 45A, number 6
PHYSICS LETTERS
5 November 1973
ical point, the central peak increases due to critical flue tuations and the side peaks shift to smaller energies merging with the central peak.
V= 420 mscc-’
We wish to thank Mr. T. Singh Narula and Mr. M. Marquardt for their technical assistence.
V.245
0.02
SCATTERING
0.06
maw-
References
0.10
VECTOR
0.14
0 [I-‘I
Fig. 2. Position of the “Brillouin peaks” as a function of Q. (a) p = 0.48 g cmm3, 70 K;(b) p = 0.98 g cme3, 40 K.
Fig. 1 presents typical spectra. A peak on the energy gain side is clearly visible. About l/3 of the central peak is due to quasi-elastic scattering on the neon; the rest is produced by elastic scattering on the container. After correction for background and for analyzer efficiency [9] also a peak on the energy loss side becomes visible. To convince ourselves that the side peaks are not spurious, the neon has been replaced by CH, gas. As expected, no peaks were observed. Fig. 2 shows that the “Brillouing peaks” shift pro portional to Q. For Q = 0.5 A--’ the peaks become unobservable. These results are compatibel with computer experiments on noble gases [lo]. Approaching the crit-
480
[l] L.D. Landau and E.M. Lifshitz, Electrodynamics of continuous media (Reading (Mass.) 1960); R.D. Mountain, Rev. Mod. Phys. 38 (1964) 205. [2] K.N. Pathak and KS. Singwi, Phys. Rev. A2 (1970) 2427; W.C. Kerr and K.S. Singwi, Phys. Rev. A7 (1973) 1043. [ 31 K.E. Larsson, Neutron inelastic scattering, (Copenhagen Symposium), Proc. IAEA, Vienna 1968, Vol. 1, p. 397 (review). [4] W.J.L. Buyers,V.F.Sears,P.A. L0nngiandD.k Lonngi, Neutron inelastic scattering (Grenoble Symposium), Proc. IAEA, Vienna 1972, p. 399. [S] D.G. Henshaw and A.D.B. Woods, Phys. Rev. 121 (1961) 1266. 161 B. Dorner, T. Plesser and H. Stiller, Disc. Faraday Sot. 43 (1967) 160. [7] K. Caneiro, M. Nielson and J.P. McTague, Phys. Rev. Letters 30 (1973) 481. [8] P.A. Fleury and J.P. Boon, Phys. Rev. 186 (1969) 244. [ 91 B. Dorner, Acta Cryst. A28 (1972) 319. [lo] A. Rahman, D. Levesque and L. Verlet, in Rivisita de1 Nuovo Cimento 1 (1969) 315.
5 November 1973
PHYSICS LETTERS
INVESTIGATION
OF COLLECTIVE
BY MEANS OF NEUTRON
EXCITATIONS
SCATTERING
AT SMALL
IN LIQUID NEON SCATTERING
VECTORS
H.G. BELL, A. KOLLMAR, B. ALEFELD and T. SPRINGER Institu t fir Festkiirperforschung
der Kernforschungsanlage,
Jiilich, 517 Jiilich, Federal Republic of Germany
Received 4 September 1973 Coherent neutron scattering on neon has been investigated above the coexistence curve for scattering vectors Q between 0.06 and 0.5 A-’ with an energy resolution of 6 X lO_’ eV. In addition to a central line, side peaks were ob served in a region of 0.06 <, Q 5 0.14 B;‘. The peaks are interpreted in terms of propagating collective excitations.
In a simple liquid one expects the existence of thermally excited collective density fluctuations which have the character of propagating waves. These modes are responsible for “Brillouin peaks” in the spectrum of scattered radiation which appear at energy transfers hw=+fivQ,
(1)
Q = k. - k, is the scattering vector, v is the velocity of propagation of these modes. In addition one expects a central line due to non-propagating fluctuations. In the case of light scattering where hydrodynamical theory holds, v is determined by the adiabatic sound velocity [ 11. On the other hand, neutron scattering allows the investigation of collective fluctuations with rather short wavelengths (N lO*A) and high frequencies & lOI sec’l) so that one can go far beyond the hydrodynamic region (cf. [2-41). By neutron spectroscopy sharp “Brillouin peaks” have been observed only on superfluid helium [5]. A weak indication of such peaks was reported for liquid Pb [6]. A number of neutron experiments has been carried out at rather large Q-values @Y0.5 A-l) so that the atomistic structure of the liquid comes into play, and eq. (1) is no longer valid. Also in this region indications of propagating,excitations have been reported, namely on various liquid metals [3] and, very recently, in a rather well defined manner on liquid parahydrogen [7]. We were able to perform neutron scattering experiments on neon at rather small scatteringvectors, namely 0.06 < Q < 0.14 A-l with a Q-resolution of 0.02 A-1 and an energy width (tivhm) of 6 X 10-S eV. These experiments are in the gap between neutron scattering experiments at large Q-values (> 0.8 A--‘) [4] where no indication of collective propagating modes has been
observed, and Brillouin scattering experiments with light [8]. Constant-Q runs were carried out at the high resolution triple axis spectrometer with double-monochromator; it is situated at one of the neutron guides on the FRJZcold source. The sample (5 cm height, 3 cm diam.) had a transmission of about 94%. The choice of a low incident energy (2.29 X lob3 eV) avoids scattering due to the first peak of the structure factor. The experimental conditions of the neon were: p = 0.48 g cm-3 = ~~withT=70K;60K;50K;45K; p = 0.75 g cm-3 with 46 K; 50 K; 55 K, and p = 0.98 g cmM3 with 40 K.
ENERGY TRANSFER
hw
lmdl
Fig. 1. Solid lines: Non-corrected neutron spectra on neon for p = pc = 0.48 g cm3 and T = 70 K, at different scattering vectors Q. Dashed line: Spectrum corrected for background and analyzer efficiency. A = energy resolution (fwhm).
479
Volume 45A, number 6
PHYSICS LETTERS
5 November 1973
ical point, the central peak increases due to critical flue tuations and the side peaks shift to smaller energies merging with the central peak.
V= 420 mscc-’
We wish to thank Mr. T. Singh Narula and Mr. M. Marquardt for their technical assistence.
V.245
0.02
SCATTERING
0.06
maw-
References
0.10
VECTOR
0.14
0 [I-‘I
Fig. 2. Position of the “Brillouin peaks” as a function of Q. (a) p = 0.48 g cmm3, 70 K;(b) p = 0.98 g cme3, 40 K.
Fig. 1 presents typical spectra. A peak on the energy gain side is clearly visible. About l/3 of the central peak is due to quasi-elastic scattering on the neon; the rest is produced by elastic scattering on the container. After correction for background and for analyzer efficiency [9] also a peak on the energy loss side becomes visible. To convince ourselves that the side peaks are not spurious, the neon has been replaced by CH, gas. As expected, no peaks were observed. Fig. 2 shows that the “Brillouing peaks” shift pro portional to Q. For Q = 0.5 A--’ the peaks become unobservable. These results are compatibel with computer experiments on noble gases [lo]. Approaching the crit-
480
[l] L.D. Landau and E.M. Lifshitz, Electrodynamics of continuous media (Reading (Mass.) 1960); R.D. Mountain, Rev. Mod. Phys. 38 (1964) 205. [2] K.N. Pathak and KS. Singwi, Phys. Rev. A2 (1970) 2427; W.C. Kerr and K.S. Singwi, Phys. Rev. A7 (1973) 1043. [ 31 K.E. Larsson, Neutron inelastic scattering, (Copenhagen Symposium), Proc. IAEA, Vienna 1968, Vol. 1, p. 397 (review). [4] W.J.L. Buyers,V.F.Sears,P.A. L0nngiandD.k Lonngi, Neutron inelastic scattering (Grenoble Symposium), Proc. IAEA, Vienna 1972, p. 399. [S] D.G. Henshaw and A.D.B. Woods, Phys. Rev. 121 (1961) 1266. 161 B. Dorner, T. Plesser and H. Stiller, Disc. Faraday Sot. 43 (1967) 160. [7] K. Caneiro, M. Nielson and J.P. McTague, Phys. Rev. Letters 30 (1973) 481. [8] P.A. Fleury and J.P. Boon, Phys. Rev. 186 (1969) 244. [ 91 B. Dorner, Acta Cryst. A28 (1972) 319. [lo] A. Rahman, D. Levesque and L. Verlet, in Rivisita de1 Nuovo Cimento 1 (1969) 315.