Experimental investigation of the premelting process in Sn

Melting of a real solid involves three stages: first comes surface melting, then the melting of grain boundaries, and finally the melting of the bulk. The first and second stages are often called “premelting.” While surface melting and bulk melting have been extensively studied, melting of grain boundaries was not. We developed an optical method which allowed us to study all three stages of melting in pure materials. Using Sn crystals and polycrystals, we were able to detect melting of the grain boundaries inside the solid around 5 K below the bulk melting temperature, and thus lead to a better understanding of how a real solid melts.

Figure 1

The experimental system. Light from the laser is partially reflected by the beam splitter, the transmitted part being absorbed by a beam dump. The reflected beam is directed into the vacuum chamber and focused by a lens of focal length 40 mm to a point above the sample surface, so that a region of the sample surface of order about 200 µm diameter is illuminated. The scattered light reflected from the surface is focused by the same lens and detected by a charge coupled device camera.

Figure 2

Maximal correlation between two simulated laser speckle patterns at $\lambda =532$ nm, scattered by an arbitrary substrate undergoing random height fluctuations of amplitude $d$.

Figure 3

Examples of two-dimensional spatial correlation between two speckle patterns of light scattered by a Sn sample at several temperatures. The area shown is about 500 µm × 700 µm. It is important to note the differences between the color scales, shown on the right of each picture. Each pair of correlated images was separated by a time interval of 120 s. The temperatures are (a) $175{}^{\circ }\mathrm{C}$, (b) $226{}^{\circ }\mathrm{C}$, (c) $227{}^{\circ }\mathrm{C}$, (d) $228{}^{\circ }\mathrm{C}$. The bulk melting point is $231.8{}^{\circ }\mathrm{C}$. While the differences between images (a)–(c) result from surface melting, image (d) at $228{}^{\circ }\mathrm{C}$ is typical of grain-boundary melting.

Figure 4

Temperature dependence of the maximum correlation between speckles of light scattered from a Pb(110) surface. The time interval between the correlated images is 120 s. The dip at $230{}^{\circ }\mathrm{C}$ is interpreted as the onset of surface melting, in agreement with [6] and [7].

Figure 5

Maximum value of the correlation between two speckle patterns separated in time by 120 s, as a function of temperature, for a (100) surface of a β-Sn crystal ($T_M=231.8{}^{\circ }\mathrm{C}).$ We identify the dip between $224{}^{\circ }\mathrm{C}$ and $229{}^{\circ }\mathrm{C}$ as due to grain-boundary melting and that at $232{}^{\circ }\mathrm{C}$ as bulk melting.

Figure 6

Maximum value of the spatial correlation between two speckle patterns separated in time by 120 s, as a function of temperature, for laser light reflected from the (110) surface of a β-Sn crystal. We identify the dip between $140{}^{\circ }\mathrm{C}$ and $210{}^{\circ }\mathrm{C}$ as due to surface melting and that between $224{}^{\circ }\mathrm{C}$ and $229{}^{\circ }\mathrm{C}$ as due to grain-boundary melting.

Figure 7

Maximum value of the spatial correlation between two speckle patterns separated in time by 120 s, as a function of temperature, for laser light reflected from the surface of a β-Sn polycrystal. We identify the dip between $226{}^{\circ }\mathrm{C}$ and $230{}^{\circ }\mathrm{C}$ as due to grain-boundary melting.

Figure 8

Time dependence of the correlation of speckle patterns over successive 60-s intervals during grain-boundary melting of a polycrystalline sample, 1.1 mm thick. The temperature at the bottom of the sample was maintained at $230{}^{\circ }\mathrm{C}$. If a grain boundary melts during the time between frames, the correlation will decrease. If nothing happens during that time, the correlation will increase. This explains the ups and downs of the data shown. Once all the GB's in the sample have melted (after about 2500 s), the sample does not change any more, the correlations increase and remain high.

Figure 9

Time dependence of the correlation of the speckle pattern over successive 60-s intervals during grain-boundary melting inside a 1.4-mm-thick polycrystalline Sn sample maintained at $229{}^{\circ }\mathrm{C}$. The high correlation after 3500 s indicates that all the grain boundaries in this sample have melted.