E. Iolin

INELASTIC NEUTRON SCATTERING BY ULTRASOUND IN SOLIDS

E. Iolin 1, B. Farago 2, F. Mezei3 , E. Raitman 1, and L. Rusevich 1

1 Institute of Physical Energetics, 21 Aizkraukles St., Riga, LV-1006, Latvia
2 Institute Laue - Langevin, BP 156, F - 38042 Grenoble Cedex 9, France
3 Hahn-Meitner Institute, Glienicker Str. 100, 14091 Berlin, Germany

Keywords: neutron scattering, ultrasound, single crystal, glasses

It is well known that thermal phonons spectrum is successfully studied by means of three -axis and TOF neutron spectrometers. The energy of ultrasonic phonons (AW) is very small, ~10^-7 eV at the AW frequency f=25 MHz. Therefore the energy spectrum of the diffracted beam could not be studied by now. Only the AW effects on the total scattering was studied. The aim of the present work was to study for the first time neutron inelastic scattering on the high-frequency ultrasonic excitations in solids. We used IN11 Neutron Spin - Echo (NSE) spectrometer at the ILL (neutron wave length l~5.4 nm, vector of scattering Q ~ 20 nm) and directly observed neutron inelastic scattering by the AW in Si single crystals, mosaic KBr crystal, pyrolitic graphite (PG), and in the glass. AW displacements U = W cos (k_sr) cos(2pf_st) were excited by means of LiNbO₃transducers. The intermediate scattering function S(t) observed by NSE could be written as

S(t) = S_{_n=0}^{^n=inf} A(n) cos (2pnft), S(0) = 1, f~f_S, I_h(n) = A(n)I_t

Here I_h(n) is the scattered beam intensity contributed by the nth harmonic. We found that experimental results are depended from quality of crystal, type of the AW (longitudinal or transversal), geometry of measurements (Laue or Bragg) and coherent properties of the AW


The measured function S(t) for perfect Si. Bragg geom., LAW, f_s=209 MHz. Elastic scattering fraction is A(0)1-A(1), A(2)=A(3)0, f/f_s=1 0.01 and W10^-4 nm/mV generator. Low frequency LAW decreases an intensity of the elastic scattering	Almost perfect Si, Laue geometry,T=400 m, LAW, f=70.3 MHz. Total It, elastic I(0), one I(1) and double I(2) phonon scattering.

The intensity of the elastic scattering I_h(0) was almost independent of the LAW amplitude at the f=209 and 148 MHz. It may be seemed surprised, an ordinary approach leads to the conclusion that the Debye-Waller factor should decrease an I_h(0). A factor exp(iQU) formed in the Takagi-Taupin eq-s exp(iQU)~ 1-f_{_pDW} - f_e + f_in ; fpDW = 1/8(QW)²; f_e= cos(2k_sr)f_pDW; shj = 2 ft tan q_B/c_s; f_in= i(QW) cos(k_sr) cos(2pf_st), DI_hpDW/I_h = - f_pDW, DI_he/I_h =+thjf_pDW

Term f_pDWdecreases an intensity of the elastic scattering on the value DI_hpDWand similar to the Debye-Waller factor. Termf_ecreates new gaps at the Dispersion Surface, that is new zones of the total elastic reflection. DI_hpDW and DI_he are the corresponding additional intensities of the elastic scattering. shj = 2f_st tan q_B (t is the extinction length, c_s-velocity of sound). These elastic satellites compensate "pseudo Debye-Waller factor" effect, the observed I_h(0) is almost independent from the LAW amplitude at the large frequency.

TAW (f_S= 154 MHz) was directed perpendicular to the scattering plane, so it doesn't effect at the intensity of the elastic Bragg peak in Si. Most of I(0) is emitted near the front and back surfaces of Si plate. The amplitude of the bulk TAW (Lamb wave) is small near these surfaces and the effect of TAW on I(0) is also small. The inelastic scattering emanates mainly in the volume of crystal. Up to 7-8 TAW orders phonons were observed in Laue geometry at the large V at 73.6 MHz.

Bent Si crystal. Lower frequency small ampl. AW (f_s=49MHz, W10^-2 nm) decreases I_h (0) by 30 %. These unusual result are in agreement with previous (1987) dynamic theory calculation.

KBr crystal. I_h(0) decreased by the TAW , f_s=111 MHz. We have to do with diffraction on independently scattering mosaic blocs, which vibrate as a whole in the AW. The main is transformation elastic scattering into one-phonon scattering by the TAW. The simple picture of AW excitation breaks down with increasing voltage (f_s=33 MHz, V200 mV).

We calculated S(t) by means of rough "quasimosaic" crystal model for the case of coherent and incoherent [3] AW. Our S(t) may be interpreted as multiple-phonon scattering by the incoherent AW.

We observed also for the first time neutron inelastic scattering by LAW, 28 MHz phonons in a glass (vitreous quartz).

In general we proposed and developed some specific extension of Brillouin scattering to AW.