The Growth Dynamics of Solid 4 He

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THE GROWTH DYNAMICS OF SOLID

4

He

CHIA-LAI WANG AND GLENN AGNOLET Department of Physics, Texas A&M University, College Station, TX 77843 ABSTRACT The interfacial properties of the solid-liquid interface of 4 He have been studied at temperatures below 0.5 K using crystallization waves. From the dispersion and damping of the crystallization waves, one can determine the interfacial stiffness, &, and the interfacial growth resistance, (Km)- 1 , respectively. Our measured values for & are consistently smaller than previously published values. At the lowest temperatures, the measured (Km)- 1 4 increases as T which is consistent with the prediction that the growth velocity is limited by the scattering of ballistic phonons by the moving interface. We also observe that above 0.25 K the phonon damping is dramatically reduced. INTRODUCTION The solid-liquid interface of 4 He is an excellent system for studying 4 crystal growth processes. He can be made extremely pure with the only known impurity being the isotope, 3 He. By simple techniques, it is easy to reduce the concentration of 3 He to below 1 part in 1015. It is also possible to grow large, high quality crystals with few defects. Another advantage of this system are the short equilibration times. Because of the vanishingly small latent heat and the superfluid properties of the liquid below 1.8 K, the interface can exhibit extremely rapid growth dynamics at low temperatures. In fact, the solid-liquid interface can support wave-like excitations that are analogous to the capillary or gravity waves found at a liquid surface. These crystallization waves propagate across the interface by alternately growing and melting the solid. As such, crystallization waves can be used as a probe of the interfacial properties. Crystallization waves were first predicted by Andreev and Parshin [1] in 1978 based on the ideas of quantum delocalization of surface defects. They predicted that the dispersion of these waves should be dominated by gravity, the surface stiffness, and the damping due to the growth coefficient K, defined as

v = mKAgi

(1)

where v is the interface velocity, m is the mass of a 4 He atom, and Ajt is the difference in the chemical potential across the interface. The functional dependence of 03(k) is given by the equation 0o2_

p' k3 _ A gk +iogk PI'P -0 2 mK(p, - p1 ) P, - P (p_ p, )2

(2)

where Ps and Pi are the densities of the solid and liquid, respectively. & is the surface stiffness and g is the acceleration due to gravity. By studying the dispersion and attenuation of these waves, one can determine the interfacial stiffness as well as the crystal growth coefficient, K. Andreev and Parshin also pointed out that the growth velocity should be limited by collisions of the rotons and phonons with the moving interface. In particular, they predicted that at the lowest temperatures, the growth resistance, (Km)-1, should increase as T4 due to the phonons scattering from the moving Mat. Res. Soc. Symp. Proc. Vol. 237. @1992 Materials Research Society

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