Squares: cooling down to 211.8 K, warming up to 245 K, cooling down to 215 K, and warming up to room temperature.
be irreversible and distribution of particle sizes should result warmed up to 237.2 K and again cooled down, the velocity in the phase transition broadening. Such an idea was manifested a jump just below the offset of melting in full used in some studies to find pore size distribution from thermocycles (Fig. 4). After the jump, the velocity branches melting processes of cyclohexane . On the other hand, corresponding to cooling and warming merged together the liquid skin model predicts that the melting process only near 270 K (Fig. 4). The effect was quite reproducible.
of a particular particle occurs within a temperature range As it has been found in previous acoustic studies of melting where the liquid layer becomes thicker . Within this and freezing in confined liquids, including confined metallic range, melting should be reversible until the offset point melts, the increase in ultrasound velocity reveals the process when the solid core melts. Therefore, the absence of the of crystallization within pores [7–9,21,22]. Thus, the abrupt reversible melting range upon warming for gallium allows increase in ultrasound velocity observed near 230 K can be us to suggest that the liquid skin model is not applicable to treated as crystallization into another gallium modification confined gallium contrary to confined mercury and isolated (or several modifications) with the offset of melting at metallic particles [7,15,16] or the melting broadening due about 270 K. It should be noted that gallium crystallizes to pore size distribution is much more essential then the near 230 K only partially. The rest part of gallium remains smearing due to liquid layer formation. liquid and freezes at lower temperatures as can be seen in According to Fig. 1 both the onset of freezing and Fig. 4.
the offset of melting for confined -gallium are shifted to To confirm the suggestion about gallium crystallization low temperatures compared to the melting point of bulk into modifications different from -Ga we carried out addi-Ga. The lowering of the offset of melting is about 21 K tional x-ray studies. The x-ray pattern obtained at 220 K afwhile for -Ga within pores in the opal  it was ter a thermocycle corresponding to the conditions described near 10 K. Since the pore sizes for the opal can be estimated above revealed additional peaks (Fig. 3, b). Most intense as 50 and 100 nm , this result qualitatively agrees with peaks (marked with 2) coincided with those belonged to a predictions of the Gibbs-Thompson equation. Taking into tetragonal modification found recently in porous glass with account the irregular shape of confined particles, affected pores of 4 nm and in artificial opals [11,12]. According by pore geometry, and particle interconnection, one can to  it has the lattice parameters a = 3.25, c = 4.hardly expect the precise accordance. Note, also, that the and differs from known bulk gallium structures . Using temperatures of the onset of freezing are almost the same in the lattice parameters a and c we can estimate the crystal the porous glass under study and in the opal (about 215 K). density assuming that the unit cell contains 3 atoms:
Acoustic studies also showed that the fulfillment of = 6.65 g/cm3. The value obtained is larger than the special conditions of thermocycling could change drastically density of liquid gallium ( = 6.095 g/cm3) similarly to the total process of gallium crystallization. For instance, other known gallium modifications except the solid -phase when the sample was cooled down to a temperature ( = 5.91 g/cm3) [17,18]. Weaker peaks (marked with lying below the onset of freezing, then consecutively in Fig. 3, b) can be attributed to the disordered -phase Физика твердого тела, 2004, том 46, вып. 2214 B.F. Borisov, E.V. Charnaya, A.V. Gartvik, Cheng Tien, Yu.A. Kumzerov, V.K. Lavrentev state at higher temperatures and can crystallize under some conditions. Such peculiar features of confined gallium are related to its ability to occur in several different crystalline modifications, which melt at particular temperatures, and with its tendency to supercooling. Rather similar behavior could be seen in bulk gallium. When gallium is supercooled at ambient pressure well below the -Ga melting point, it can crystallize into -Ga . It is also known that supercooled bulk gallium crystallizes below 303 K into the modification upon cooling as well as upon warming if heterogeneous nucleation was initiated. The fact that the process of additional crystallization in confined gallium at about 230 K was observed only after preparatory cooling below the onset of ordinal freezing near 215 K (Fig. 4) shows the importance of the presence in pores of a small amount of frozen gallium. One can suggest that such crystallites serve as nucleation centers, which provoke Figure 5. Temperature dependences of the NMR signal heterogeneous crystallization. One can also suggest that intensity I for three thermocycles started at room temperature. Cirthermal conditions used in the present studies influence the cles — cooling down to 204 K, squares — to 208 K, diamonds — to 212 K. Open and closed symbols correspond to cooling and geometry and number of crystallites to make possible the warming, respectively. The straight lines are guides for the eye.
crystallization near 230 K.
In conclusion, studies of freezing and melting for gallium confined within a porous glass with 8 nm pore size showed that the solidification and melting transitions upon deeper following x-ray data published in  for gallium embedded cooling until complete freezing started at about 215 K are into artificial opals. Three other peaks (marked with x) were due to formation of -Ga within pores. The melting and not identified. Thus, according to the x-ray data obtained, freezing temperature ranges were noticeably down shifted the hysteresis loop I in Fig. 4, b arises due to formation compared to the bulk -Ga melting point. Both melting of -Ga while the hysteresis loop II is related chiefly with and freezing were irreversible. The irreversibility of melting crystallization into the tetragonal modification and to a lesser contradicts the liquid skin model and allows suggesting that extent into -Ga and into a unidentified phase.
the melting process broadening arises mainly due to pore According to acoustic studies, freezing at about 230 K size distribution, contrary to the case of confined mercury.
into the tetragonal and modifications could also occur The results obtained also revealed that fulfilling some when the sample was cooled down to a temperature lying special thermal conditions leads to gallium crystallization at below the onset of freezing and 204 K (with the rate less about 230 K into the tetragonal gallium modification which than 15 K/h below about 235 K and less than 40 K/h at was found intil now only in confined geometry and into other temperatures) and consecutively warmed (Fig. 4, b).
the disordered phase. The fact that the crystallization It should be expected that the decrease in the total needs in some amount of crystallites of another confined amount of liquid gallium caused by partial crystallization gallium modification to start, evidences an important role of at about 230 K can be detected by NMR. While precise heterogeneous nucleation in freezing within pores.
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