Effect of surface roughening on liquid-solid interface velocity
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I. INTRODUCTION Recent pulsed-laser experiments1"3 on the melting and freezing of silicon have raised fundamental questions regarding interface motion at high velocities. Real-time x-ray diffraction measurements1'2 on both (100) and (111) surfaces have shown that no measurable overheating is required to melt at a speed of 11 m/s, but about 80 K undercooling is needed to achieve a freezing velocity of 5 m/s. However, no such asymmetry was found in transient conductivity experiments3 involving amorphous silicon formed by ion implantation of (100) crystalline silicon. Conventional transition-state theory4 (TST) predicts no asymmetry for small departures of temperature T from the melting point TM. (Asymmetry specifically means departure from the relation |v| = f(\T - TM\) where v is the interface velocity with the convention v > 0 for freezing and v < 0 for melting, and the functional relationship states that the speed |v| is the same for a given amount of undercooling or overheating.) I have recently shown5 (referred to as PR) that if the difference in density between liquid and solid is accounted for, large asymmetry can result for \T - TM\ 3= 25 K, although the slope of v vs TM — T is continuous at T = TM and, henceforth, defined as /3. Such large asymmetry results from the assumption that excess density cannot all be transported from the interface at the speed of sound. Some diffusive hops are required. This slower rate of density transport results in a buildup of density excess at the interface and concomitant pressures of the order of 10 kbar. These points, which must be regarded as starting hypotheses, are discussed at length in PR. New x-ray data on germanium6 suggest the asymmetry may be highly anisotropic (anisotropy as used here refers to dependence on crystal orientation and should not be confused with "asymmetry"). The slope of v vs T — TM was about four times greater for melting than for freezing of a (111) surface, but no asymmetry was seen for the (100) surface. The anisotropy reported in Ref. 6 was for freezing only; the (111) and (100) surfaces had the same v vs T for melting, within experimental error. A larger slope of v vs T upon freezing was also observed for the (100) surface of silicon than for the (111) in Ref. 2, although no overheating was
detected there for either surface. Recent molecular dynamics simulations7'8 have further indicated the (111) surface of silicon recrystallizes more slowly than the (100). There is thus a body of evidence in support of the freezing velocity being greater for (100) than for (111), while the situation in regard to anisotropy of melting may be more in doubt. The present paper shows that anisotropy can result from the fact that the (111) surface is smooth while the (100) surface is rough or faceted.91 show that the density effect, which causes both asymmetry and a decrease of /3, can be much more effective for a smooth than a rough surface. The physical idea is as follows. Since the liquidsolid transition rate is density dependent, it is influenced by fluctuati
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