The present work was partially supported by the National Science Council of Taiwan under Grant 91-2112-M006-017.
1. Introduction while freezing could be quite sharp. However, contrary to the case of confined mercury and other liquids, the Recently, a great deal of attention was focused on studies hysteresis loops observed for gallium within most of of surface and size effects induced by confined geometry. porous matrices were complicated with two or more steps Properties of materials embedded into nanoporous matrices upon cooling and warming. Later x-ray studies showed were shown to differ remarkably from those in bulk. that gallium in nanometer-size pores can crystallize into In particular, metals confined within porous glasses and different modifications [11,12]. Note that bulk gallium artificial opals manifest alterations in their superconducting also occurs in different crystalline phases [17,18]. Under behavior [1–3], atomic mobility in melted state , melting ambient pressure, bulk liquid gallium crystallizes into -Ga and freezing processes [5–9], electronic features  and with the melting point of 303 K and the supercooled in crystalline structure [11,12]. Studies of melting and melt can freeze into -Ga (the melting point 256.5 K).
freezing of metals in confined geometry revealed some Other bulk crystalline modifications occur only under high common features such as noticeable reduction of the phase pressure. Solid modifications of gallium submicrometric transition temperatures and rather reproducible thermal droplets coincide with the bulk ones . According hysteresis upon cooling and warming. These changes in to [11,12,20] confined gallium modifications depended on behavior of confined metals were similar to anomalies upon pore size and geometry. They included the bulk - and melting and freezing for simple and organic liquids within -gallium as well as some modifications with symmetry nanoporous matrices observed until now (see [13,14] and different from known bulk gallium structures. In particular, references therein). Some other properties were specific a tetragonal modification  was observed in artificial for melting and freezing in particular metals. For instance, opals and in porous glasses with pore size of 4 nm.
acoustic and NMR measurements on mercury in porous Polymorphism of confined gallium explained the complex glasses were treated within the model of liquid skin formed character of its freezing and melting transitions. However, upon melting [7,8] similarly to melting of isolated metallic the processes of simultaneous or consecutive crystallization particles [15,16]. into various modifications and their interrelation with pore The melting and freezing processes of gallium in confined geometry and thermal history are not clear until now.
geometry were studied in [9,11,12] and in references The reduction of the gallium phase transition temperatures therein. First NMR, acoustic, calorimetric and resistance and irreversible melting agreed according to [9,11] with measurements carried out for gallium embedded into ar- predictions of the Gibbs-Thompson equation developed tificial opals and porous glasses with 4 and 200 nm pore for isolated small spherical particles. Nevertheless, the sizes revealed noticeable depression of the melting and coexistence within pores of various crystalline species freezing temperatures compared to the melting point of along with their structure disordering and some other bulk -gallium accompanied with pronounced hysteresis. experimental facts discussed in [11,12] prevented the quanThe melting process was reported to be strongly broadened titative treatment. Another aspect of gallium solidification Peculiarities of gallium crystallization in confined geometry which was discussed in [9,11,12] concerned the nature of nucleation (homogeneous or heterogeneous) in confined geometry and reasons for thermal hysteresis upon cooling and warming. While experimental results obtained in  allowed suggesting the significant role of hetergeneous crystallization within pores, the matter remained unclear until now.
The aim of the present paper is to study using acoustic, NMR, and x-ray methods the melting and freezing processes for gallium in a porous glass with about 8 nm pores in connection with the problems stated above.
2. Experimental Figure 1. Pore zise distribution in the porous glass under study according to mercury intrusion porosimetry.
Samples of porous glass used in the present work were prepared of phase-separated soda borosilicate glass with pore structure produced by acid leaching. The pore size found to be equal to 8.4 nm by mercury intrusion and 295 K. During measurements the temperature was porosimetry and small angle x-ray scattering. The pore stable within 2 K. The x-ray patterns were recorded within volume distribution versus pore diameter according to an angle range 20 to 80 degrees with the scan speed mercury porosimetry is shown in Fig. 1. The liquid gallium of 0.5 deg/min.
was introduced into pores under high pressure up to 10 kbar.
The filling factor of the pore volume was near 85%.
3. Results and discussion Numerous acoustic investigations of porous matrices filled with liquids showed that the velocity of longitudinal Temperature dependence of intensity of Ga NMR line as well as transverse ultrasonic waves changes noticecorresponding to liquid gallium upon cooling from room ably upon melting or greezing of embedded materials temperature down to 160 K and consecutive warming for following changes in effective elastic moduli of the samthe rate of changing temperature between measurements ples [7–9,21,22]. This allows the use of acoustic methods of about 50 K/h is presented in Fig. 2. It shows that for detailed studies of the melting and freezing processes confined gallium starts freezing at about 215 K and the in confined geometry. We employed the conventional pulse solidification process ends at about 165 K. Upon warming, ultrasound technique  at the frequency of 7 MHz, which the melting process becomes noticeable only above 195 K gave the relative longitudinal sound velocity value and the total amount of gallium melts near 235 K. Note that smooth alterations in the NMR signal intensity outside v/v = v(T ) - v(T = 295 K) v(T = 295 K) with an accuracy better than 10-5. All measurements were made during continuous slow cooling or warming the sample within a range 295 to 160 K with various rates of changing temperature. The temperature gradient in the sample did not exceed 0.05 K/cm.
NMR measurements were carried out using a pulse Bruker Avance 400 NMR spectrometer. The Ga NMR signal corresponding to liquid gallium was observed at various stabilized temperatures in the range 295 to 160 K.
Since the integral intensity of the signal is proportional to the total amount of melted gallium, NMR provides direct information on the fraction of liquid and solid gallium phases within pores. The operating frequency was 122 HMz. The temperature was controlled within 0.5 K.
Prior to each measurement, the sample was kept at a fixed temperature for about 5 minutes. To detect NMR line, a single pulse sequence with phase cycling was applied with pulse duration of 2.5 µs. The repetition time was 0.1 s.
Figure 2. Temperature dependences of the NMR signal intenThe x-ray diffraction measurements were performed sity I (circles) and relative ultrasound velocity v/v (triangles) for using a commercial powder diffractometer DRON-2.0 with the full freezing-melting thermocycle upon cooling (open symbols) CuK radiation at several temperatures between 180 and warming (closed symbols).
7 Физика твердого тела, 2004, том 46, вып. 2212 B.F. Borisov, E.V. Charnaya, A.V. Gartvik, Cheng Tien, Yu.A. Kumzerov, V.K. Lavrentev of thermal history on the melting and freezing processes for confined gallium. The measurements disclosed that, when thermocycles started at room temperature and cooling continued down to below 204 K, the main hysteretic behavior was reproducible independently of the cooling or warming rate. Namely, freezing started near 215 K and the offset of melting was seen near 235 K. It was also obtained that both melting and freezing were completely irreversible, that is when crystallization was interrupted at some intermediate temperature and the sample under study was warmed up, the velocity curve upon warming did not coincide with that upon cooling but merged with the warming branch of the full hysteresis loop at higher temperatures. An example is shown in Fig. 4, a. Similarly, when the sample was cooled down after incomplete melting, the velocity curve tended Figure 3. X-ray powder diffraction patterns obtained at 211 K (a) to merge with the cooling branch of the full hysteresis loop.
upon cooling from room temperature and at 220 K (b) after conNote, that the irreversible freezing in confined geometry was secutive cooling down from room temperature to 205 K, warming also seen in other liquids [7,13,22] and can be explained up to 240 K, cooling down to 190 K, and warming up to 220 K.
by hysteresis between freezing and melting. However, a Peaks corresponding to -Ga, the tetragonal modification, -Ga temperature range of reversible melting was found upon and to a unidentified structure are marked with 1, 2, 3 and x, warming for some liquids in porous matrices including respectively.
mercury [7,8,13] contrary to the results obtained for gallium in the present and previous studies.
Normally the treatment of the melting and freezing of the gallium phase transitions obviously rise due to the phase transitions for confined liquids is based on moCurie law for nuclear susceptibility. The full hysteresis loops dels developed for isolated spherical or cylindrical partiupon cooling and warming with similar rate of changing cles [8,13,21,22]. Simple theories predict reduction of the temperature were quite reproducible, the temperatures of melting or freezing points for small paticles because of the onset and offset of the phase transformations shifted a large surface to volume ratio. For spherical paticles for no more than several degrees. Measurements of the melting temperature depression Tm is given by the temperature dependences of ultrasound velocity for similar Gibbs-Thompson equation  thermocycles also showed hysteresis loops associated with Tm = 2v0Tb/Lr, (1) the melting and freezing processes (Fig. 2) which agreed well with the NMR data.
where r is the particle radius, is the surface tension As can be seen in Fig. 2, both the melting and freezing of the solid, L — is the latent heat of fusion, Tb is the processes are noticeably lowered compared to those for bulk bulk melting temperature, and v0 is the molar volume of -Ga and smeared over large temperature ranges. X-ray the solid. Freezing is mostly treated as a result of supermeasurements showed that the freezing observed is related cooling. This explains the hysteresis between solidification with formation within pores of a single crystalline modiand melting and therefore, the irreversible behavior upon fication coincided with -Ga. The x-ray pattern obtained freezing. However the geometric-freezing model was also at 211 K after cooling from room temperature is shown in discussed for porous media [22,27]. According to this Fig. 3, a.
model, crystallization in confined particles is considered The width of peaks in Fig. 3, a was greater than the similarly to structural phase transformations in solids. Then instrumental broadening (0.3). Hence, following [11,12] it is controlled by pore geometry and the depression of the one can evaluate the average size of confined metallic freezing temperature Tf for spherical particles is given by crystallites from the peak broadening using the Scherrer equation . The obtained size of about 25 nm is Tf = 3v0Tb/Lr, (2) noticeably larger than the pore diameter. This means that the crystallization front passes through gallium within where is the surface energy. However, the geometseveral neighbor pores. Similar difference in pore diameters ric-freezing model can not provide an appropriate explanaand crystallite sizes was also found for gallium in other tion for the hysteresis. A more complicated analysis implies nanoporous matrices [11,12], for indium in Vycor glass  the formation of a liquid layer (liquid skin) surrounding the and for some wetting liquids such as O2, D2 and CO2 solid core of a small particle (see [16,28] and references (see  and references therein) in contrast to confined therein).
mercury . The relationships (1) and (2) predict that the phase Using acoustic methods we then performed detailed transitions occur at a temperature determined by the particle studies of influence of the rate of changing temperature and radius. Thus the total processes in confined geometry should Физика твердого тела, 2004, том 46, вып. Peculiarities of gallium crystallization in confined geometry Figure 4. Temperature dependences of the relative ultrasound velocity v/v upon cooling (open symbols) and warming (closed symbols) for thermocycles started at room temperature. The straight lines are guides for the eye. a) Triangles: cooling down to 194.4 K, warming up to room temperature. Circles: cooling down to 204.7 K, warming up to 237.2 K, cooling down to 203.7 K, and warming up to room temperature. b) Diamonds: cooling down to 204.4 K, warming up to 235.5, cooling down to 232 K, and warming up to room temperature.
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