COHERENT NEUTRON SCATTERING FROM POLYCRYSTALS

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COHERENT NEUTRON SCATTERING FROM

POLYCRYSTALS

U. Buchenau, H. Schober, R. Wagner

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C6, supptdment au n O 22, Tome 42, ddcembre 1982 page C6-395

COHERENT NEUTRON S C A T T E R I N G FROM POLYCRYSTALS

U. Buchenau, H.R. Schober and R. Wagner

Ins t i t u t fiir Festktirperforschung der KernforschungsanZage JiiZich, Postfach 191 3, 0-51 70 JiiZich, F.R. G.

Abstract.- Phonon dispersion curves are mostly determined by co- herent neutron scattering from single crystals. For a number of materials, however, large enough single crystals are not obtaina- ble. We used the detailed structure of the coherent scattering from polycrystals to obtain as much information on thephonons as possible. Time-of-flight spectra of A1 and Ca over a large area in Q and w have been analyzed in terms of lattice dynamical models. It turns out that, at least for these simple materials, a rough picture of the phonon dispersion may be obtained.

It is well known that phonons can be measured by coherent inelastic neu- tron scattering from single crystals. Much less is known about the in- formation contained in the coherent inelastic scattering from polycry- stals. Two special cases have been considered earlier: the region of high momentum transfer where the phonon spectrum may be obtained and the regions of low energy transfer near Debye-Scherrer rings where ela- stic constants can be determined

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In this work we show that by mea- suring in an extended range of energy and momentum transfer one may even get a rough picture of the full phonon-dispersion

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at least in the simple cases considered, namely polycrystalline A1 and Ca at room temperature.

A L U M I N U M 2 9 3 K

Experiment

Detector Nr. Time of Flight Detector Nr.

Time of Flight Fig. 1: Time-of-flight spectrum of polycrystalline A1 at 293 K

C6-396 JOURNAL DE PHYSIQUE

Fig. 1 shows measured and calculated time-of-flight spectra for Al. The intensity rise at short flight times corresponds to the onset of one-phonon annihilation processes at the maximum lattice frequency of about 10 THz. The upper boundary of the time range corresponds to 3 THz. The momentum transfer increases with increasing detector number and decreases with increasing time of flight. In the region shown above it ranges from 2 to 6

8-I.

The experiment was done on the time-of- flight spectrometer SV5 at the cold source of the reactor DIDO in Ju- lich (wavevector of incoming neutrons 1.31 4 range of scattering angles 20 to 160 degrees)

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The theoretical spectrum was obtained using a set of Born-v. Kar- man parameters from the literature 3. The one-phonon scattering con- tributions on a fine mesh through the relevant Brillouin zones were summed up (using the symmetry as far as possible) and folded with the instrumental resolution. The result agrees reasonably well with the experiment, though there are some distinct differences. A better agree- ment can be achieved by fitting the Born-v.Karman parameters to the experiment. We did this assuming axially symmetric springs extending up to the sixth nearest neighbour and using the known elastic aon- stants 4 . Multiphonon and multiple scattering were calculated using simple approximations. The result is summarized in Table 1. Fig. 2 shows that this fitted parameter set reproduces the experimental dis- persion along the symmetry directions astonishingly well.

Fig. 3: Phonon dispersion and phonon spectrum in Ca at 293 K.

Table 1 and Fig. 3 show fit results for Ca at room temperature. No single crystals of this material are available because of its martensi- tic phase transformation at 720 K. The elastic constants determined at low energy transfer with the method2 c1 =25+3 GPa, cl 2=1 521 GPa and dq4=20+1 GPa were included in the fit. The resulting bulk modulus -18.3 GPa is in reasonable agreement with the static value of 17.2 FPa. The phonon dispersion shown in Fig. 3 corresponds rather closely to pseudopotential calculations if these are scaled down by 16%.

f > Neighbour and A1 Ca indices 1 XX 10056.+100. 3806.250. 1 ZZ -985.- -133. 1 XY 11038. 3939. 2XX 1364.+100. -1513 2Yy 90. 227. 3 XX -629 .+50 250.220. 3YY -1 9. 94. 3YZ -203. 52. 3x2 -407. 104. 4xx 107. 422 -470. 4XY 577. 5XX 149. 5YY -53. 5ZZ -78. 5XY 76. 6XX 57. L 6Y Z -145. References

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492 (1966) C.Kitte1, Intr. to Solid State Physics, 2.ed., p.99, Wiley, New York 1963

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