QUANTUM DIFFUSION IN SOLID HELIUM, DETECTION AND INVESTIGATION OF IMPURITON-PHONON MECHANISM OF SCATTERING

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QUANTUM DIFFUSION IN SOLID HELIUM, DETECTION AND INVESTIGATION OF IMPURITON-PHONON MECHANISM OF

SCATTERING

B. Eselson, V. Mikheev, V. Grigoriev, N.P. Mikhin

To cite this version:

B. Eselson, V. Mikheev, V. Grigoriev, N.P. Mikhin. QUANTUM DIFFUSION IN SOLID HELIUM, DETECTION AND INVESTIGATION OF IMPURITON-PHONON MECHANISM OF SCATTER- ING. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-119-C6-120. �10.1051/jphyscol:1978654�.

�jpa-00218027�

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JOURNAL DE PHYSIQUE Colloque ^C6,supplgment au no 8, Tome 39, aozit 1978, page C6-119

QUANTUM DIFFUSION

I N

SOLID HELIUM, DETECTION

AND

INVESTIGATION O F IMPURITON-PHONON MECHANISM O F SCATTERING

B.N. Eselson, V.A. Mikheev, V.N. Grigoriev and N.P Mikhin Physico-TechnicaZ Institute of Low Temperatures, UkrSSR Academy of Sciences, 47, Lenin Prospect, Kharkov, 310169, USSR

R6sumB.- On mesure par la mQthode des Qchos de spin en RMN le coefficieqt de diffusion D de 3 ~ e dans 4 ~ e solide pour des concentrations x en 3 ~ e comprises entre 6 x 10 1,2 x Les rQsul- tats obtenus montrent que pour x <

lo-"

D augmente brusquement lorsqu'on abaisse la tempdrature T suivant la loi D a T - ~ , ce qui rQvPle le r81e dominant de la diffusion des phonong par les impuretQs.

Par diverses mdthodes on Qvalue la largeur de la bande d'impuritons 1 environ 104 ~ . Abstract.- The diffusion coefficient, D, of 3 ~ e in solid 4 ~ e with the concentration of

6 x 5 ^X( 1.2 r 10 3has been measured using the pulse NMR method. The results suggest that for the 3 ~ e concentration less than there is a sharp increase in D with lowering the temperature by the law D c T - ~ , indicating the dominant role of the processes of lattice phonon scattering of impuritons in solid helium..Estimated by various methods, the energygap of impuritons is about c 10 4 ~ .

Numerous recent experimental studies in pro- perties of quantum crystals are related to the theoretical prediction /I/ of some new effects cau- sed by a quantum behaviour of defect and impurity mobility in such crystals. The effect of quantum diffusion of impurities found some years ago when studying the diffusion in a hcp-phase of helium iso- top solid solutions should be first mentioned.

In the case of quantum diffusion bounded by the collisions between impurity quasi-particles (impuritons) the diffusion coefficient D of 3 ~ e is temperature independent /2,31 and increases in in- verse proportion to the 3 ~ e concentration /2,4/.

Using a new NIQ method, we succeeded recently in detecting /5/ and studying the increase of D by the law D ~ T - ~ with decreasing the temperature, which was due to the lattice phonon scattering of impuritons. The measurements were carried out in the 3 ~ e concentration range of 6 x 1 0 ~ ~ 9 2.17 x The results on the temperature dependence of D are shown in figure 1. Clearly defined are the main re- gularities describing the diffusion in quantum crystals : an exponential decrease in D with reducing the temperature, which is due to the vacancy mechanism (curves 4-61, a sharp increase in D with decreasing the temperature in dilute solutions with the 3 ~ e content of & 10-3 ; it is related to the phonon gas scattering of the impuriton gas (curves

1-2) ; and D(T) = const. at low temperatures when the impuriton-impuriton collisions become dominant.

To make a quantitative comparison between the

theory and the experiments, the experimental data on D(T) were treated assuming that the impuriton- impuriton collision is independent of the impuriton-phonon collision /2,6/.

Fig. 1 : Temperature dependence of diffusion coef- ficieht of 3 ~ e in solid 4 ~ e at different 3 ~ e con- centrafions : I-X = 6x10-~; 2-X = 5.2x10-~; 3-X =

1.2~10 (present results, V=20.95 cm3/mole) ; 4-X = 2.5x10-~; 5-X = 7.5~10 3 ; 6-X = 2.17x10-~

(results from our work 131, V=20.7 cm3/mole) For a solid helium of V=20.95 cm3/mole, the diffu-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978654

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sion coefficient in a quantum region appeared to References obey the equation

( 1 ) /I/ Andreev,A.F. and Lifshits,I.M., Zh. Eksp. Teor.

D - ~ = lxl0l1~ + 4 . 1 ~ 1 0 ~ ~ ~ c m ~ / s . Fiz.

56

(1969) 2057 which describes the temperature and the concentra-

/2/ Grigoriev,V.N., Eselson,B.N., Mikheev,V.A. and tion dependences of D (figure 2). Shulman,Yu.E., Pisma v ZhETF

17

(1973) 25

Fjg. 2 : Concentration dependence of diffusion coef- flcient of 3 ~ e in solid 4 ~ e (V=20.95 cm3/mole) in the region of impuriton-impuriton interaction. The data for X > 1.2x10-~ were taken from 131.

/3/ Grigoriev,V.N., Eselson,B.N. and Mikheev,V.A.,

The existence of "phonon" and "impuriton" scattering portions in Curves 1 and 2 (figure 1) permits the energy gap of impuritons to be estimated for each mechanism of quasi-particle interaction, A E = zI3~(I3~is the exchange integral of 3 ~ e - 4 ~ e , z is a number of nearest neighbours).

Estimation of AE by the formula for the diffusion coefficient 17-1 bounded by the phonon scattering of impuritons gives A E % I O - ~ K and, respec- tively 131, % I O - ~ K . Note, that 131, estimated for the impuriton-impuriton scattering 181 gives the same order of magnitude.

It should be mentioned that the value of I34 estimated by the above methods is approximately 10 times less than 133 for pure 3 ~ e with a given molar volume 191.

Zh.Eksp

.

Teor. Fiz.

66

(1974) 321

/ 4 / Richards,M.G., Pope,J. andWidom,A., Phys. Rev

Lett.

2

(1972) 798

/5/ Mikheev,V.A., Eselson,B.N., Grigoriev,V.N. and Mikhin,N.P., Fiz. Nizk. Temp.

3

(1977) 385 161 Andreev,A.F., Usp. Fiz. Nauk

118

(1 976) 251 /7/ Pushkorov,D.I., Fiz.Nizk.. Temp.

1

(1975) 586 /8/ Sacco,J.E., Widom,A., Locke,D. and Richards,

M.G., Phys. Rev. Lett. 37 ⁽¹⁹⁷⁶⁾760 /9/ Gueyr,R.A., Richardson,R.C. and Zane,L.I.,

Rev. Mod. Phys.

9

(1971) 532

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