FOURTH INTERNATIONAL SYMPOSIUM

SCATTERING OF NEUTRONS

M . G . Z e m l y a n o v

ON INELASTIC

An international symposium on inelastic scattering of neutrons dealing with results of research on the dynamics of the condensed state of matter over the past three years, using neutron scattering techniques, was held in Copenhagen in May, 1968, under joint auspices of IAEA and the Denmark atomic energy corn- miss ion.

Over 200 sc ient is ts were in attendenee, to hear 102 pape r s . The agenda included: 1) solid s ta te dy- namies ; 2) dynamics of liquids; 3) magnet ic sy s t ems ; 4) molecu la r dynamics ; 5) exper imenta l techniques.

The g rea t e s t number of r epo r t s on any one topic dealt with so l id-s ta te dynamics , and could be sub- divided under three headings: meta l s , nonmetals , imper fec t c rys t a l s . Dynamics of meta ls were t rea ted in some noteworthy papers on m e a s u r e m e n t s of the phonon spec t r a of lithium (Oak Ridge, USA) and rub i - dium (McMasters Univ., Canada)~ These papers provided a complete p ic ture of the dynamics of the alkali me ta l s , since the phonon spec t r a in sodium and po tass ium had been m e a s u r e d ea r l i e r .

Analysis of the resu l t s based on the Born - - yon Karman model showed that six coordination spheres have to be taken into account to provide an adequate descr ip t ion of the phonon spect rum~ Two of the repor t s dealt with exper imenta l de terminat ion of Cohen s ingular i t ies . T e a m s of Swedish sc ient i s t s were the f i r s t to successfu l ly obse rve Cohen s ingular i t ies in the case of a univalent meta l (copper). One of the in teres t ing pape r s in this group of paper s was p resen ted by Bo Brockhouse and S. Ngo (McMasters Univ.) on i n v e s t ~ a - tion of the v ibra t ional spec t rum in alloys of bismuth: lead, and thall ium (binary and t e rna ry alloys). Since the m a s s e s of these e lements differ only slightly, any changes mus t be due to d i f ferences in the i r va lency . The phonon spec t rum is readjus ted smoothly in these alloys, following the e lec t ron concentrat ion fa i r ly r igorous ly . Two complete ly different alloys having the same e lec t ron density will have c lose ly s i m i l a r phonon spectra.

Of the other theoretical papers deserving special mention, we note two reports submitted by the Soviet delegation. One (Yu. Kogan, E, Brovman) analyzes the role of electrons in the formation of the phonon spec- trum of metals. Attention was focused on proving the existence of unpaired coupling between covalent type ions in metals, a consequence of the interaction of three or more ions simultaneously through conduction electrons. This case provided a successful explanation of practically all experimental results within the framework of a unified approach. The second report (E. Brovman et al.) developed a general theory of vibrations in hexagonal-lattice metals, taking indirect coupling between ions, either paired or unpaired, into account. The authors were successful in accounting for the principal singularities in the spectra of such metals as beryllium, magnesium, and zinc, for the first time.

The paper on dynamics of nonmetals which impressed us most was submitted by O. Syngh et al, (Univ. of Iowa, USA), presenting results of a study of He 4- (single crystal) dynamics. Dispersion curves for wave vectors along the C axis were measured and all four branches were determined. The width was compara- tively small in the case of acoustical branches, but amounted to one-third of the maximum longitudinal op- tical frequency. As might be expected, intense anharmonic coupling was observed. An Austrian team (Seibersdorf, reactor center) presented a report on the effect of pressure on the phonon spectrum of Na!. Clashing with the earlier value on Nal, their data indicated no negative Griineisen constant up to 3 kbar.

A good deal of attention was given to the dynamics of irregular systems, a branch of solid-state physics which has been undergoing vigorous development in the past few years. A paper by R. Niklov et al. (Oak Ridge) discussed the dynamics of the single-crystal alloys Cu l_xAlx, with x = 4.1% and 10%. First success was reported in detecting an additional peak corresponding to a local level on the curve giving cross section as a function of energy transfer at a fbxed transferred momentum. The position of the local

Trans la t ed f r o m Atomnaya l~nergiya, Vol. 26, No, 1, pp. 84-87, January , 1969.

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frequency indicated no change in the force constants. Two of the papers discussed research on vanadium alloys. A paper by B. Moser (USA) reported a most interesting result in the case of a V + Be alloy. The local level was found and asymmetric splitting of the peak in response to a rise in concentration was de- tected and attributed to the structure of the impurity band. A paper submitted by M. Zemlyanov et al~ (USSR) cited results on V + Ta and W alloys. The authors reported success in observing a quasilocal fre- quency for both these alloys. The energy position of this frequency was in satisfactory agreement with isotopic substitution model calculations. The alloy containing W impurity also revealed a shift on the en- tire spectrum toward higher frequencies, compared to the spectrum of V and V + Ta. This shift probably stems from a change in the electron density of the alloy as a result of the introduction of impurity atoms of different valency than the matrix atoms. V. Beyers and R. Cowley (Chalk River, Canada) studied neu- tron scattering on mixed KBr + RbBr crystals containing 20~ c and 50% of the second component. A slight frequency shift and a change in width were observed in the transverse branch when the RbBr was introduced. Longitudh~al vibrations in the (Ill) direction showed a more sensitive response.

Investigations of the liquid state showed that the patterns of diffusional motion differ markedly from the classical mode of motion, i.e., continuous motion, even in the case of the simplest liquid systems, such as liquid sodium and liquid argon~

In the case of complex molecular liqui~Is, we observe a superposition of the diffusional and rotational motions of the molecule as a whole, and this adds severe complications to interpretation of the results and to comparison with data obtained in other independent experimental research.

Experiments on coherent scattering of neutrons by simple liquids were of special interest. The simi- larity in the spectra of neutrons scattered coherently from polycrystalline and liquid specimens suggests some phonon-like collective excitations in liquids. Analysis of the experimental data points to the existence of averaged dispersion relations between energy and momentum of longitudinal collective excitations in some simple liquids, similar to the excitations existing in the corresponding polycrystalline specimen.

Some papers reported data on high-frequency transverse waves in liquids~ But a theoretical descrip- tion capable of accounting for the experimental findings is still lacking. Best agreement with experiment is obtained with the Egelstaff model in which existence of both longitudinal and transverse collective excita- tions is postulated, and which allows introduction of the "lattice" concept applied to liquids. This is empha- sized most vividly in a paper by S. J. Cocking (Britain) applying the quasiphonon treatment to analysis of data on coherent scattering of neutrons by liquid lead. But some authors approach the introduction of the "lattice" concept In the theory of liquids with much caution~ Hence the attempts by these authors to devise a theory of high-frequency density fluctuations in liquid are of paramount Interest. These projects are still in a rudimentary stage of development, and are still far from providing an explanation of the available ex- perimental data.

Another particularly interesting paper was presented by A. Woods and R. Cowley (Canada) on high- energ~j excitations in liquid helium. This paper represents the first experimental attempt to detect the "Bose condensate, " i.e., helium atoms in the ground state and accordingly possessing zero momentum, in the superfluid state. The experimental complexity of this approach lies in the fact that the number of such atoms ts mInute. Preliminary results indicate that ~10% of the total number of atoms are found in the "con- densate" state; this is in satisfactory agreement with theoretical calculations,

Impressive advances in the field of molecular dynamics (over the progress reported at previous sym- posia) were registered in the investigation of coherently scattering molecular systems, either single crys- tals or quasisingle crystals. This research paved the way for measuring the dispersion curves relating to certain symmetry directions, thereby making it possible to compare experimental and predicted results more correctly, and to reach conclusions on the adequacy of our concepts referable to molecular systems of the type investigated. A team of American scientists presented measurements of dispersion relations for skeleton vibrations in deuterated polyethylene. Parallel orientation of the axes of molecular chains was achieved by stretch-forming polycrystalline polyethylene (misalignment of axes ~-.9~ The results were qualitatively in agreement with model-based calculations taking Into account optical measurements data, even though the calculated data turned out somewhat too high. B. Powell (Canada) reported measurements of dispersion curves for deuterated hexamethylenetetramine in the symmetry direction A, A, ~, and D. The results are explained satisfactorily by a simple model which takes into account nearest neighbors of the first and second coordination spheres, and was put forth by V. Cochrane and C. Pawley.

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Also of interest was a paper by W. Whitmore reporting an investigation of polyglutamide acid (PGA) and its sodium salt (NaPGA). PGA and NaPGA belong to the class of polypantides, which exhibit many proper t ies s imilar to the proper t ies of natural proteins. A repor t by W. Clay dealt with a study of DNA and straightened polynucIeotide filaments by inelastic s c a t t e r i n g of cold neutrons. But the resul ts p r o , sented in the two reports do not allow of an exhaustive interpretation at this stage and should be regarded as tentative, while constituting sufficient evidence that neutron scat ter ing techniques are s tar t ing to come into their own as useful tools in the study of the microdynamics of b iopolymers .

For the f i rs t time, a large number of papers on magnetic sys tems (sixteen in all) was presented at the symposium. A review paper by M. Bje r rum-Mol le r (Denmark) cited r e sea rch findings on r a r e - e a r t h metals and 3d-transi t ion metals, and presented some arguments on the mos t profi table trends for r e s e a r c h on magnetic mater ia ls . In the iron group, this r e s e a r c h trend would be high-energy excitations, st~dy of which would reveal more details on exchange interaction and effects owing to the nature of magnetic e lec- trons. In r a re earths, the trend of interest would be the study of magnetic spec t ra over a broad temperature range with magnetic field effects included. A detailed study of spin waves and lifetime as a function of the tempera ture could yield information on the relationship between conduction electrons and magnetic in terac- tion. A study of the lifetime Of spin waves in the ferromagnet ic phase, specifically, would:shed some light on the effect of ordering on exchange splitting of the energy band. Information on the energy band Of condue- tinn electrons would also be helpful in computing exchange coupling between magnetic ions a:c~d in computing ion decay.

Several repor ts dealt with measurements of the dispersion curves of spin waves (COO, a -Co) , a - C o resul ts were in agreement with I. Low's calculated based on the model of localized electrons with Heisen- be rg -Di rac type exchange interaction taken into account. These calculations imply a quadratic dispersion curve governed by a unique pa rame te r D whose value is the same for all directions of symmet ry investi- gated.

Some of the papers submitted dealt with the behavior of magnetic mater ia ls near the Critical t emper - ature. N. Kroo (Hungary) cited data on the spec t ra of MnO spin waves near the Neet tempera ture (109-207~ The neutron inelastic scat ter ing spec t rum experiences no change in the transit ion through TN, indicating the presence of collective excitations in the paramagnet ic phase. Some basical ly new information on mag- netic sys tems was provided by a study of dynamics utilizing scat ter ing of polar ized neutrons. There was only one paper (O. Steinvol, Norway) on investigation of magnet ic-vibrat ional waves in an iron single c r y s - tal by the polar ized neutron method. Polar izat ion effects in diffuse neutron scat ter ing were shown to be determined by inelastic p rocesses . The widths of diffuse reflections are in k~rmony v, t~h the linear d i s - pers ion law for phonons, while the speed of sound recovered f rom these measurements is in harmony with data a r r ived at by independent measurements . The proposed method can be used, in principle, to find the magnetic form factor of the ion; measurements are now being conducted toward that end.

A paper presented by N. Kroo (Hungary) on the formation of virtual spin-wave states in dilute alloys (3%) of iron (Mn, Er , V, Cr) and nickel (V, Cr) was met with interest . In all these alloyS, with the sole exception of Fe(V), a resonant virtual level was detected. Assigning a Lorentz shape to the line, the authors calculated the lifetime of this virtual state. The lifetime was found to be 0.5-10 -l'~ sec, in the case of Fe (Mn), and ranging to 6.6.10 -12 sec in the case of Fe (Er)o T h e lifetime is somewhat longer than would be expected for a Heisenberg insulator in the case of Fe (Cr), and this is apparently due to the effect of the conduction electrons.

Experimental r e sea rch techniques and appropriate experimental a r rangements and setups were dis~. cussed at a special session of the symposium. Seventeen repor ts were directed to this topic, three Of the most Interesting being presented by L. Pal (Hungary), G. Cauldwe[1 (USA), and F:o Hompf (West Germany), These papers suggested using stat is t ical techniques of the type used in investigations of kinetic phenomena in nuclear reac to rs for t ime-of-f l ight neutron spec t romet ry r e sea rch . P re l imina ry experiments have shown that these s tat is t ical techniques br ing about an appreciable increase (sixty-fold) in spec t romete r luminosity and reduction (sLxteen-fold) in background. This opens up new possibili t ies for measur ing weak effects against a disturbingly s trong background.

A high-precision spec t rometer for very cold neutrons was discussed in a paper by V. Aifeld (West Germany). The author successful ly attained a resolution of 7.2:10 -5 for 2- 10 -~ eV neutrons by using a neutron guide (35 m long) and large reflection angles (~90 ~ on a silicon single c rys ta l , This is the best

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resolution attained to date in neutron spectrometers. This spectrometer opens up a basically new area

of investigation for various types of hyperfine splittings in the solid state and liquid state.

Roberts describing polarized neutron spectrometers were submitted for the first time. The polarizer and analyzer were Co(Fe) single crystals, and bursts of polarized neutrons were generated by employing a Flynn device placed between the first and second crystals. The spectrometers can be used in experiments with bursts of monochromatic and polarized neutrons. The duration of the bursts and the repetition rate are determined electronically, and are accordingly adjustable over a broad range.

There were many papers on description of new devices utilizing already familiar techniques of neu- tron monochromatization and neutron analysis, and some describing improvements in systems already available. One of the most interesting of these papers was presented by M. Wilkinson (USA) on a triaxial crystal spectrometer installed at the Oak Ridge HFJR reactor. A special RDR-8 machine takes full charge of spectrometer control, and control of the accessory equipment as well. The arrangement was designed for research at both high and low temperatures, simultaneous analysis of polarization and scattered-neu- tron energy, work with polarized and unpolarized neutrons. The spectrometer described is the most ad- vanced and sophisticated of its type and opens up a broad range of possibilities for research along various lines in solid state physics where neutron scattering is a useful tool. Advances in experimental research techniques using neutron scattering are due in large measure to the performance of the neutron source used (flux level and spectral distribution of the neutrons).

Local shaping of the slow-neutron spectrum, which can greatly augment neutron flux at a certain neutron energy by shifting the temperature of the original spectrum, was discussed in papers submitted by O. Abeln (West Germany) and F. Davies (Britain). The former paper cited data on a hot neutron source installed at the FR-2 reactor (Karlsruhe). The moderator is graphite, and heat released by radiation pro- vides the necessary heating of the source. Graphite heated below 1000~ does not raise neutron flux, and at 1540~ the increase in the flux of E = 0.33 eV neutrons is about 7. Hot neutron sources are of interest in research on high-energsT states in metals, alloys, molecular systems, and in cryogenic research. The latter paper describes a cryogenic source of cold neutrons in use at the HERALD reactor in Aldermaston. The use of a liquid-phase hydrogen-- deuterium mixture five liters in volume made it possible to increase the flux of neutrons of wavelength 6-15 A twenty to thirty times. The reported increase was much greater (by about ten times, in fact) that that reported earlier at other research centers.

The symposium proceedings will be published in 1969.

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