Crystal nucleation in undercooled liquid zirconium

Abstract

Electromagnetic and electrostatic levitation are applied to undercool melts of pure Zr. Each sample is undercooled approximately 100 times and the distribution functions of undercoolings are determined. They are analyzed within a statistical approach of classical nucleation theory. Despite large undercoolings the analysis predicts heterogeneous nucleation in electromagnetic levitation. Electrostatic levitation leads to an increase of average undercooling and the statistical analysis indicates that the undercoolings approach the limit as given by homogeneous nucleation.Crystallization of liquids is a first-order phase transition and initiated by nucleation. The activation barrier of nucleation controls the undercooling level measured in experiments. One distinguishes between heterogeneous nucleation and homogeneous nucleation. Heterogeneous nucleation is an extrinsic process in which container walls and/or foreign phases in the melt participate in. In contrast homogeneous nucleation is an intrinsic process, in which the undercooled liquid and the solid nucleus are involved. Hence, heterogeneous nucleation is governed by the experimental conditions whereas homogeneous nucleation depends on the properties of the system investigated.In the present work we apply electromagnetic ͑EML͒ and electrostatic levitation ͑ESL͒ techniques to investigate the maximum undercooling of pure Zr. Using these containerless processing methods heterogeneous nucleation on container walls is completely circumvented. Samples were processed by about 100 heating and cooling cycles in both experimental setups. The probability distribution of undercoolings measured in both levitators are analyzed within a model of Skripov. 1 The evaluation of the undercooling distribution functions yields the activation energy of crystal nucleation and the density of nucleation sites. Both quantities were found to be different for EML and ESL experiments. The results are discussed with respect to the physical nature of nucleation observed in both different sets of experiments.Sphere like Zirconium samples were prepared from ingot material purchased from Teledyne Wah Chang with a purity of 99.995% cut into pieces and melted in an arc furnace made of UHV compatible stainless steel components under high purity Ar gas ͑6N͒. For EML ͑Ref. 2͒ the samples of 8 mm in diameter are processed in an ultrahigh vacuum chamber, which is evacuated to a pressure of 10 −7 mbar before backfilling with He gas with a purity of 6N. The compensation of the gravitational force implies a minimum power absorption to levitate the sample. Heat radiation is not sufficient to transfer the heat produced in the electromagnetically levitated sample and to cool it below its melting temperature. Therefore, cooling by forced convection with He of high purity is used to cool the sample. For ESL, 3 samples of 2 mm in diameter are processed under ultra high vacuum conditions ͑Ϸ2 ϫ 10 −8 mbar͒. Levitation and heating is decoupled in contrast to EML. In both levitation setups the temperature is measur...

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

“…The stochastic nature can be used to obtain information on the underlying nucleation kinetics by measuring the statistical fluctuations in the undercooling. When a melt is cooled down below its melting point, the undercooling at which solidification occurs typically follows a Poisson distribution and the distribution of undercooling values, typically over a 10-20 K range, 24,[27][28][29] can be used to derive the nucleation rate as a function of temperature. 30,31 In the present case, the Bi and In solidification peaks are highly reproducible, indicating a more deterministic solidification process.…”

“…By contrast, many studies of metal undercooling go to great lengths to minimize nucleation through use of small spherical samples suspended in vacuum or surrounded by a flux. 24,[27][28][29] Because so many nucleation events occur during solidification of a thin-film sample, the calorimetry trace can be regarded as a cumulative superposition of traces obtained for many individual nucleation events, and analysis of the shape of the solidification peak should provide information on nucleation statistics. There are, however, a number of other factors that influence the shape of this peak including the temperature uniformity across the sample area and the temperature oscillations of the AC measurement, 15 making the analysis somewhat involved and beyond the scope of the present manuscript.…”

Non-Equilibrium Solidification of Undercooled Metallic Melts

“…Only the negentropic model by Spaepen is in agreement with the experiments. More details are given in [21]. …”

Scanning AC Nanocalorimetry and Its Applications

“…The stochastic nature can be used to obtain information on the underlying nucleation kinetics by measuring the statistical fluctuations in the undercooling. When a melt is cooled down below its melting point, the undercooling at which solidification occurs typically follows a Poisson distribution and the distribution of undercooling values, typically over a 10-20 K range [60,[63][64][65], can be used to derive the nucleation rate as a function of temperature [66,67]. In the present case, the Bi and In solidification peaks are highly reproducible, indicating a more deterministic solidification process.…”

“…The very large interface-to-volume ratio of a thin film provides ample opportunity for heterogeneous nucleation as confirmed by the polycrystalline structure of the samples after solidification. By contrast, many studies of metal undercooling go to great lengths to minimize nucleation through use of small spherical samples suspended in vacuum or surrounded by a flux [60,[63][64][65]. Because so many nucleation events occur during solidification of a thin-film sample, the calorimetry trace can be regarded as a cumulative superposition of traces obtained for many individual nucleation events, and analysis of the shape of the solidification peak should provide information on nucleation statistics.…”