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Submitted on 1 Jan 1978
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FLUID STRUCTURE FACTOR MEASUREMENTS IN 4He AT T = 10 K
B. Weiss, H. Robkoff, R. Hallock
To cite this version:
B. Weiss, H. Robkoff, R. Hallock. FLUID STRUCTURE FACTOR MEASUREMENTS IN 4He AT T
= 10 K. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-217-C6-218. �10.1051/jphyscol:1978696�.
�jpa-00218376�
JOURNAL D E PHYSIQUE
Colloque C6, supplement an n" 8, Tome 39, aout 1978, page C6-217
FLUID STRUCTURE FACTOR MEASUREMENTS IN *He AT T = 10 K
+. tf ttt
B.L. Weiss , H.N. Robkoff and R.B. Hallock
Department of Physios and Astronomy University of Massachusetts, Amherst, Massachusetts OlOOZ USA
Résumé.- Nous présentons nos premiers résultats expérimentaux du facteur de structure fluide de ''He à T = 10 K et à des densités de 62,7 et 110 kg/m3. L'extrapolation de nos résultats à un transfert de moment nul est en accord avec les prédictions de la thermodynamique.
Abstract.- We report preliminary results for the fluid structure factor of "*He at a temperature of 10 K and densities of 62.7 and 110 kg/m3. Our results extrapolated to zero momentum transfer are consistent with expectations based on thermodynamics.
Information on the pair correlation function and the experimentally accessible fluid structure factor, S(k), of ""He at temperatures above 5 K is sparse. Several theoretical calculations of the pair correlation function have been carried out, but experimental results are rare /1,2/. In an effort to study ''He at temperatures near and above the criti- cal point, we have begun a systematic series of mea- surements of the fluid structure factor as a func- tion of both density and temperature. Here we pre- sent preliminaty results for S(k) at T = 9.99 K and the two densities 62.7 and 110 kg/m3.
The measurements were carried out using a re- cently completed x-ray spectrometer /3/ designed for the study of cryogenic liquids where 0.3 K<\,T and the pressure, P, of the fluid sample is £ 3 MPa. A Rigaku RU-200PL rotating anode x-ray machine is used as a source of an intense beam of CuK x-rays.
a The scattered x-rays are detected by means of an intrinsic Ge detector cooled to 77 K and the main beam intensity is monitored through the use of a Xe - Co2 filled proportional counter. The spectro- meter resolution for these measurements was selec- ted to be 0.02 A_ 1. The target cell which contai- ned the helium studied in these measurements was constructed from high purity grade N-50-C beryllium.
The geometry was a cylinder with I.D. = 1.27 cm and wall thickness 250 ym. Temperatures were measu- red by means of a germanium resistance thermometer previously calibrated over the range 1.5 K<T<100 K.
Observed pressure values were converted to densi- ties by use of the tabulated work of McCarty Ikl.
The fluid structure factor, S(k), is obtai- ned from the observed scattering intensity, I(k) through the use of /5/
l(k)p*f (a' + a'.) a.
S(k)
I'(k)pf a
(O
where p represents the number density, f a trans- mission factor, k the momentum transfer and the o's are the coherent (e) and incoherent (i) scatte- ring factors for helium. The primes represent these same quantities for neon /5/ gas at 77 K and a pres- sure of 9.1 x 101* Pa. The use of neon gas allows geometric factors in the scattering to be elimina- ted experimentally. Neon is a useful choice for this purpose since at this temperature and pressure its structure factor is unity (to within 1/2 %) over the whole momentum transfer range. The inten- sity values used in eq. (1) were corrected for mul- tiple scattering effects /6/ at each value of the momentum transfer. The fluid structure factor va-
lues presented in figures 1 and 2 have not been smoothed and the error bars in the figures repre- sent the effects of counting statistics alone. They are larger at larger momentum transfer values due to the weak intensity of coherent scattering from helium at large scattering angles. Systematic errors from vaious sources are also present and we estima- te these to be about 4 %.
In each case, the data are consistent with the intercept S(k=0) = pk TX_ expected from ther- modynamics. Here p is the density, k_ the Boltzman constant, T the temperature and X_ the isothermal compressibility. The intercept shown on the figures is obtained from the work of McCarty. The data are Supported by the National Science Foundation
,. through DMR 77-07727
Present address : Bell Telephone Laboratories, ... Holmdel, New Jersey
On leave until September 1978 at the Laboratory of Atomic and Solid State Physics, Cornel Uni- versity
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978696
seen to be consistent with expectations although References a quantitative comparison awaits more closely spa-
ced data and data at smaller values of the momen- /I/ Hallock,R.B., Phys.Rev.
9
(1973) 2143tum transfer. /2/ Achter,E.K. and Meyer,L., Phys.Rev.
188
(1969) 291/3/ Robkoff,H.N., Weiss,B. and Hallock,R.B., Rev.
Sci. Instrum. (to be published)
/4/ McCarty,R.D., J.Phys.Chem.Ref. Data 2 (1973) 923
/S/ See, for example, Hallock,R.B., Phys.Rev.
(1972) 320
Fig. I : The fluid structure factor of 4 ~ e at 9.99 K and density 62.7 kg/m3. The error bars are due to counting statistics alone. The k=O intercept is obtained from the thermodynamic tabulations of McCarty / 5 / .
/6/ Weiss,B.L., Ph.D. Dissertation(Univ. of Mass.
1977, unpublished)
Fig. 2 : '~e fluid structure factor at 9.99 K and density l l0kg/m3.
