On the twinning occurrence in bulk semiconductor crystal growth

Based on known theories of twinning in semiconductor crystal growth, a new model is proposed to study the occurrence of twins during the solidification of photovoltaic multicrystalline silicon ingots. It is expected that twins will appear on facets existing at the grain boundary–solid–liquid triple line. Necessary conditions for the existence of facets are derived and it is shown that twinning remains a function of the probability of nucleation of twinned nuclei. It is demonstrated that this probability is in qualitative agreement with the experimental observation for cases where the grain orientation is such that an angle of 132° occurs between a facet and a grain boundary. However, full validation of the model requires accurate values of interfacial energies at the melting point, which are currently lacking.     

Transition metal co-precipitation mechanisms in silicon

Formation mechanisms of precipitates containing multiple-metal species in silicon are elucidated by nano-scale morphology and phase investigations performed by synchrotron-based X-ray microprobe techniques. Precipitates formed at low (655 °C) and high (1200 °C+) temperatures exhibit distinguishing features indicative of unique formation mechanisms. After lower-temperature annealing, co-localized single-metal silicide phases are observed, consistent with classical models predicting that dissolved, supersaturated metal atoms will precipitate into solid second-phase particles. Precise precipitate morphologies are found to depend on the local crystallographic environment. In precipitates formed during slow cooling from higher-temperature anneals, nano-scale phase separation and intermetallic phases are evident, suggestive of a high-temperature transition through a liquid phase. Based on experimental results and phase diagram information, it is proposed that under certain conditions, liquid metal–silicon droplets may form within the silicon matrix, possibly with the potential to getter additional metal atoms via liquid–solid segregation.     

The effect of vanadium and grain refiner additions on the nucleation of secondary phases in 1xxx Al alloys

High purity Al–0.3 wt% Fe–0.1 wt% Si alloys with different Si, V and grain refiner contents were melt spun to produce microstructures of submicron secondary phases entrained in a higher melting point Al matrix. On reheating, a dispersion of eutectic liquid droplets forms that represents an exaggerated version of the liquid puddles that solidify pinched-off between Al dendrite arms during conventional casting. The subsequent resolidification of the droplets, analysed using differential scanning calorimetry (DSC), allows the nucleation-controlled aspects of secondary phase selection to be studied. The droplets solidify as the metastable FeAl_m phase in ribbons containing ≃500 ppm V or ≃100 ppm V plus Al–Ti–B, Al–Ti–C or Al–B grain refiner. This phase contributes to the “fir-tree” surface defect in commercial sheet products. This work suggests that the combination of V and Al–Ti–B promotes FeAl_m in commercial ingots, and confirms that solidification rate and bulk Si content also influence phase content.     

Nucleation kinetics of continuously cooling Fe–17 at.%B droplets produced by controlled capillary jet breakup

A new method for the investigation of the nucleation kinetics of traveling droplets was applied to mono-size droplets of an Fe–17 at.%B alloy generated by a controlled capillary jet breakup process. The developed method determines the in-flight nucleation kinetics of droplets from metallographic data and simulated droplet-cooling schedules. An iterative procedure is used to cross-validate the metallographic data and the model predictions. With the cross-validated data and simulation models, nucleation temperatures of Fe–17 at.%B droplets were calculated for various diameters and cooling conditions and shown in the form of continuous-cooling transformation (CCT) diagrams. The critical cooling rate for the amorphous solidification of Fe–17 at.%B droplets was predicted as a function of droplet diameter and verified metallographically.     

Composition and non-equilibrium crystallization in partially devitrified co-rich soft magnetic nanocomposite alloys

The body-centered cubic (bcc) phase tends to preferentially nucleate during solidification of highly undercooled liquid droplets of binary alloy systems, including Fe–Co, Fe–Ni and Fe–Cr–Ni. We investigate a similar tendency during the partial devitrification of Co-rich amorphous precursors of composition (Co_1?xFe_x)₈₈Zr₇B₄Cu₁ by identifying the structure and composition of the nanocrystalline grains. The Co:Fe ratio of the bcc nanocrystals varies linearly with the Co:Fe ratio of the amorphous precursor, and can lie well within the single-phase face-centered cubic (fcc) region of the Fe–Co phase diagram at the crystallization temperature. Classical nucleation theory therefore suggests several potential explanations for the preferential nucleation of bcc phase from an amorphous precursor, including: (i) a reduced amorphous/bcc interface energy as compared to the close-packed phases; (ii) a lower strain of precipitation for bcc nuclei as compared to close-packed fcc and hexagonal close-packed nuclei; and (iii) stabilization of the bcc phase by dissolved glass-formers such as Zr and B.     

偏晶合金液-液相变过程模拟

建立了能描述在弥散相液滴形核、扩散长大、碰撞凝并及两液相空间分离等因素共同作用下，偏晶合金液-液相变过程中组织演变过程的数学模型。将计算的温度场和浓度场与控制凝固组织演变的动力学方程相耦合，模拟研究了单向冷却条件下Al-Pb合金液-液相变过程中的组织演变过程。结果表明，随着冷却的进行，液-液相变区不断由试样底部向试样顶部推进，直至贯穿整个试样。由于在凝固过程中弥散相液滴进行Marangoni迁移和Stokes运动，试样中的某些部位会出现液滴贫化、过饱和度增加和多次形核现象。     

Effect of semisolid microstructure on solidified phase content in 1xxx Al alloys

Melt-spun high purity Al–0.3 wt% Fe–0.1 wt% Si alloys, containing V and Al–5Ti–1B grain refiner, were melted at 2 K/min from 635°C to different temperatures above the solidus in a differential scanning calorimeter (DSC). Quenched and slow cooled (at 2 K/min) microstructures were examined using scanning electron microscopy (SEM). Melting was observed in a hot-stage reflected light microscope. Al–Fe₄Al₁₃ melted first, forming cell boundary liquid films. Rapid coarsening occurred at <4 K above the solidus via motion of these boundaries. Intracellular liquid droplets formed at 4–6 K above the solidus. These droplets have been demonstrated to be sites of metastable Al–FeAl_m formation in V and Al–5Ti–1B containing alloys on solidification. With increasing temperature the liquid cell boundaries thickened and consumed the droplets, until there were none left at 10 K above the solidus, when the microstructure was fully molten. Consequently Al–FeAl_m only formed in V and Al–5Ti–1B containing alloys when solidified following melting to 4–10 K above the solidus.     

The effect of silicon on the nanoprecipitation of cementite

The current work presents a comprehensive study that aims at understanding the role of silicon on θ precipitation, as well as on the ε → θ carbide transition in tempered martensite. Cementite nucleation was modelled under paraequilibrium conditions in order to ensure the presence of silicon in the carbide, where both thermodynamic and misfit strain energies were calculated to evaluate the overall free energy change. The growth stage was investigated using in situ synchrotron radiation; three alloys containing 1.4–2.3 wt.% silicon contents have been studied. Silicon appears to play a significant role in carbide growth. It was observed throughout tempering that cementite precipitation was slower in the higher silicon content alloy. Literature reports that cementite growth is accompanied by silicon partitioning, where the silicon content inside the carbide decreases as tempering progresses. Therefore it appears that the limiting factor of the growth kinetics is the rate at which silicon is rejected from the carbide; the silicon piles up at the carbide–matrix interface, acting as a barrier for further growth.     

Early stages of intermetallic compound formation and growth during lead-free soldering

We investigate the early stages of the morphological evolution of intermetallic compounds (IMCs) during lead-free soldering involving liquid Sn-based solder and Cu substrate considering the heterogeneous nucleation of the IMCs. The simulation is performed through the multi-phase-field approach [20], [25]. Initially, the liquid Sn-based solder and the Cu substrate are considered to be at metastable local equilibrium. Nucleation at the solder/substrate interface is modeled by considering it to be a Poisson process. The phase-field simulation accounts for variations in grain boundary diffusion in the η phase and interface energies between the η phase and liquid solder, and uses these variations to investigate the multiplicity of soldering reactions, and make comparisons with previous work [23]. The simulations address the kinetics of the IMC growth during lead-free soldering under the effect of nucleation at an early stage, illustrating the variation in Cu substrate thickness, IMC thickness and number of grains that nucleate or disappear due to grain growth-induced coalescence.     

Direct evidence for the formation of ordered carbides in a ferrite-based low-density Fe–Mn–Al–C alloy studied by transmission electron microscopy and atom probe tomography

We study the structure and chemical composition of the κ-carbide formed as a result of isothermal transformation in an Fe–3.0Mn–5.5Al–0.3C alloy using transmission electron microscopy and atom probe tomography. Both methods reveal the evolution of κ-particle morphology as well as the partitioning of solutes. We propose that the κ-phase is formed by a eutectoid reaction associated with nucleation growth. The nucleation of κ-carbide is controlled by both the ordering of Al partitioned to austenite and the carbon diffusion at elevated temperatures.     

Levitated Liquid Dynamics in Reduced Gravity and Gravity-Compensating Magnetic Fields

Dynamic models are used to investigate the behavior of liquid droplets suspended in alternating current and direct current magnetic fields in microgravity and in various configurations providing conditions similar to microgravity. The realistic magnetic fields of solenoidal coils are used for the modeling experiments with electrically conducting (liquid silicon or metal) droplets. At high values of magnetic field, some oscillation modes are damped quickly, while others are modified with a considerable shift of the oscillating droplet frequencies and the damping constants from the nonmagnetic case. On a larger scale, the models are used to investigate the melting and heating process of reactive materials. It is demonstrated how 1?kg of liquid titanium in a traditional ??cold?? crucible-type furnace can be fully levitated without contact to wall to achieve high superheat of the melt.     

Temperature and structure dependency of solid–liquid interfacial energy

A new model has been proposed for the prediction of solid–liquid interfacial energy for pure elements. It is assumed that the interface between crystalline solid embryo and bulk liquid consists of a monolayer of atoms having a similar atomic packing factor as that of the crystalline solids. It has been observed that the solid–liquid interfacial energy is a strong function of temperature and structure of the solid and planar density of the interface. The solid–liquid interfacial energy has a lower value close to melting temperature and it reaches a maximum at some intermediate temperature. This model tries to correlate the classical nucleation phenomena and structure model of interfaces.     

Influence of nucleation and growth phenomena on microstructural evolution during droplet-based deposition

In the present study, Phase Doppler interferometry (PDI) is utilized to measure droplet sizes and velocities, which are used as initial conditions in the following calculations. A numerical approach, along with the microstructural observation, is implemented to analyze the heat transfer, nucleation and growth of individual droplets during both flight and deposition. The results confirm that during the initial deposition stage, a second nucleation event can occur in the remaining liquid of impinging droplets. The two nucleation events generate intermixed small and large grains at the end of solidification, in agreement with the experimental observation. After a mushy layer forms, no second nucleation can occur. The deposited material's surface behaves like a size modulator which regulates and equalizes the different-size nuclei within impinging droplets. Grains grow from the surviving nuclei, and their growth fronts converge thereby producing a relatively equiaxed grain morphology.     

Do substitutional solutes soften or embrittle cracktips in α-Fe?

We employ atomistic modeling to examine the influence substitutional solutes have on the activated process of nucleating dislocations from cracktips in α-Fe. We demonstrate a strong correspondence between the energy landscape of the solute during an idealized block-like sliding process and the influence on the activation energy barrier for dislocation emission near a idealized cracktip. Using a series of solute potentials developed with input from ab initio calculations, these models predict that Cu and Ni both lower the activation energy barriers for emission, while solutes such as Mo and W raise the barriers. For solutes that raise or lower the emission barriers, the implications on the overall nucleation frequency turns out to be very different.     

Interface reaction in the B4C/(Cu–Si) system

The instability of boron carbide in contact with liquid copper triggers the interaction between B₄C and the melt. In a silicon-free melt, this interaction leads to the dissolution of boron in the liquid Cu with a concomitant release of free carbon. The compositions of the substrate and of the melt are adjusted according to the equilibrium requirements in the three-phase (B₄C–graphite–liquid solution saturated with carbon) system. In the course of the interaction between boron carbide and the Cu–Si melt containing less than 13 at.%Si, no silicon carbide is formed and the liquid does not wet the substrate. For a silicon content higher than 13 at.%, the presence of graphite particle agglomerates within a crater, which is formed as a result of the initial decomposition of boron carbide, offers appropriate sites for the nucleation and subsequent growth of SiC particles. The interaction between the Si-containing melt and the B₄C substrate leads to an enrichment of the melt with boron released from the substrate. In the vicinity of the triple line, the composition of the near-surface substrate layer is shifted to higher boron content and the conditions for wetting the substrate are met.     

Microstructure Evolution of a Ternary Monotectic Alloy During Directional Solidification

A model was developed to describe the microstracture evolution in a directionally solidified ternary monotectic alloy.The directional solidification experiments were carried out on Al-3Pb-lSn(wt%) alloys by using a Bridgman apparatus.The microstracture evolution in the directionally solidified sample was calculated.The numerical results agree well with the experimental ones.It is demonstrated that the nucleation of the minority phase droplets occur at two different positions.One corresponds to the liquid-liquid decomposition,which occurs in front of the solidification interface.The other is at the liquid/solid interface.The nucleation rate of the minority phase droplets at the liquid/solid interface is significantly higher than at the position in front of the solidification interface.The characteristic of the nucleation process leads to a bimodal size distribution of the minority particles in the directionally solidified sample.     

Transmission electron microscopy and thermodynamic studies of CaO-added AZ31 Mg alloys

We investigated the microstructural evolution of Mg–3Al–1Zn (AZ31) alloy systems, with Ca or CaO added, by carrying out microstructural characterizations in conjunction with thermodynamic calculations. A calculated phase diagram of the Mg–Ca–O ternary system showed that CaO can be dissolved in liquid Mg so as to have 12.6 wt.% Ca content in the liquid Mg at 700 °C. Therefore, for a 0.3 wt.% CaO-added AZ31 alloy, our thermodynamic calculation predicted a similar precipitation pathway to that of a 0.3 wt.% Ca-added AZ31 alloy during the solidification process. In fact, a thermodynamic analysis of the precipitation pathway assuming the Scheil model showed that the major precipitates in both alloys were Al₈Mn₅, CaMgSi, Laves C15 and Laves C36, in good agreement with our experimental observation. However, a microstructural characterization of the as-cast alloys using transmission electron microscopy revealed that the spatial distribution of the precipitates was significantly different in the two alloy systems; unlike in the Ca-added AZ31 alloy, the Ca-containing precipitates in the CaO-added AZ31 alloy exhibited strong agglomeration tendencies. Moreover, in an alloy solidified at a faster cooling rate, undissolved CaO particles were observed in the precipitate agglomerates that were connected to the other Ca-containing precipitates. These results suggest that an incomplete dissolution of CaO particles in the liquid results in the agglomeration of precipitates, as the undissolved CaO particles can act as local sources, supplying Ca to the liquid, and can thus act as preferential nucleation sites for the Ca-containing precipitates forming during the solidification of the alloy.     

Analytical treatment of diffusion during precipitate growth in multicomponent systems

We propose an approximate growth rate equation that takes into account both cross-diffusion and high supersaturations for modeling precipitation in multicomponent systems. We then apply it to an Fe-alloy in which interstitial C atoms diffuse much faster than substitutional solutes, and predict a spontaneous transition from slow growth under ortho-equilibrium to fast growth under the non-partitioning local equilibrium condition. The transition is caused by the decrease in the Gibbs–Thomson effect as the growing particle becomes larger. The results agree with DICTRA simulations where full diffusion fields are calculated.     

High-Precision Nucleation Rate Measurements for Higher Melting Metals

Nucleation of a crystal in undercooled melts of higher melting face-centered-cubic-metals has often been studied in the past. However, the data available were not of sufficient accuracy and only covered nucleation rates in too small of a range to allow precise conclusions concerning the nature of the underlying process as well as concerning important parameters such as the solid–liquid interface free energy that can in principle be deducted from such analyses. One way to circumvent ambiguities and analyze nucleation kinetics under well-defined conditions experimentally is given by performing statistically significant numbers of repeated single droplet experiments. Application of proper statistics analyses yields nucleation rates that are independent of a specific nucleation model. The first studies that were conducted in accordance with this approach on pure model materials revealed that the approach is valid. The results are comparable to those obtained by classic nucleation theory applied to experimental data, and it was shown that one might need to rethink the common assumption that heterogeneous nucleation is almost always responsible for solidification initiation. The current results also show that often-used models for the solid–liquid interface free energy might lead to overestimated values.     

Model for calculation of microstructural development in rapidly directionally solidified immiscible alloys

A model has been developed for the calculation of the microstructural evolution in a rapidly directionally solidified immiscible alloy.Numerical solutions have been performed for Al-Pb immiscible alloys.The results demonstrate that at a higher solidfication velocity a constituteional supercooling region appears in front of the solid/liquid interface and the liquid-liquid decomposition takes place in this region.A higher solidification velocity leads to a higher nucleation rate and ,therefore,a higher number density of the minority phase droplets.A s a result,the average radius of droplets in the melt at the solid/liquid interface decreases with the solidification velcity.