Liquid–Solid Phase Transition in Discontinuous Metal Films

Abstract

The thermodynamics of the liquid–solid phase transition in small particles in the size range where the phase transition hysteresis vanishes, is considered. The crystallization of small droplets in discontinuous films of tin, lead, bismuth, and gallium is studied experimentally. The fraction of the crystallized particles is determined from the temperature dependence of the integral intensity of one of the reflections of the electron diffraction pattern. The experimental results are compared with the theory of homogeneous nucleation at the crystallization of supercooled liquids.

Correlations between Surface and Interface Energies with Respect to Crystal Nucleation

“…In the particular case of Ga, the undercooling is large enough (θ ≈ 0.50) using the dispersion technique (30) to occur very near to the nose of the θ − C n curve. Since the maximum value for C n (i.e., for θ = 2/3) diminishes with K * V , the scaling supports the possibility for extremely small Ga droplets, through favorable characteristic times, to stay liquid (i.e., to bypass the nose) at the temperature of liquid nitrogen as realized by Koverda et al (31). As a last remark, undercooling experiments are quite systematically performed by continuous cooling of the melt until nucleation.…”

Nucleation rates of Sn in undercooled Sn-Ag-Cu flip-chip solder joints

“…15 with a best fit line. 28 Extrapolations of this line to temperatures of the present study indicate negligible nucleation rates for high purity Sn samples such as those utilized in Skripov's study at temperatures near 200 C. Furthermore, the temperature dependences of nucleation rates of Sn in small, high purity Sn droplets, and in SnAgCu flip chip solder joints are very different (Fig. 15).…”

“…Such models assume that the structure of sub critical clusters in multi-component supercooled liquids is generally different than that of the equilibrium solid. [27][28][29][30][31][32][33] The nucleation rate of Sn in these SnAgCu samples was sensitive to thermal history. A distinct change in the nucleation kinetics (a 44% decrease in the value of W in Eq.…”

“…[12][13][14][15]28 Data from previous work (described as homogeneous nucleation by Skripov et al) for high purity Sn samples are represented in Fig. 15 with a best fit line.…”

“…It is generally observed that the rate of nucleation of a supercooled liquid increases exponentially as the degree of undercooling increases, for undercooling of up to 0.2 T m and more. [12][13][14][23][24][25][26][27][28][29] In fact, classical nucleation theory 23,24,29 provides an expression for the heterogeneous nucleation rate, I het , in an undercooled liquid which indicates that these rates rapidly increase as undercooling increases…”