The nucleation and growth of SiC precipitates in liquid silicon is important in the crystallization of silicon used for the photovoltaic industry. These processes depend strongly on the carbon concentration as well as the equilibrium solubility relative to the precipitate phase. Here, using a suite of statistical thermodynamic techniques, we calculate the solubility of carbon atoms in liquid silicon relative to the β-SiC phase. We employ several available empirical potentials to assess whether these potentials may reasonably be used to computationally analyze SiC precipitation. We find that some of the Tersoff-type potentials provide an excellent picture for carbon solubility in liquid silicon but, because of their severe silicon melting point overestimation, are limited to high temperatures where the carbon solubility is several percent, a value that is irrelevant for typical solidification conditions. Based on chemical potential calculations for pure silicon, we suggest that this well-known issue is confined to the description of the liquid phase and demonstrate that some recent potential models for silicon might address this weakness while preserving the excellent description of the carbon-silicon interaction found in the existing models.

The inducer is often used to prevent cavitation in a centrifugal pump. However, it may lead to deterioration of the cavitation performance of the pump when poorly matched with the impeller. Numerical simulations are employed to study the effects of the matching, specifically, the axial space and the circumferential deflection between the inducer and the impeller, on the cavitation performance. The results show that the inducer destroys the rotational symmetry of the velocity distribution at the inlet of the impeller, resulting in the influence of cavitation on the part of the channels in advance, which explains why the inducer cannot improve the cavitation performance even though it improves the inlet energy of the impeller. On the basis of not changing the geometric shape of the inducer and the impeller, the suction-specific speed is increased by nearly 300 by only adjusting the axial space and by nearly 100 by only adjusting the circumferential deflection. The cavitation performance is better with a larger axial space. There is an optimal value of the circumferential deflection at which the pump works at the best cavitation performance. The effect of the axial space on the overall cavitation performance is more significant than that of the circumferential deflection. The results provide a useful reference for the design and installation of a centrifugal pump inducer.

It has long been suggested that the familiar intrinsic point defects (vacancies and self-interstitials) encountered in crystals at low temperatures ($T$) transform into extended domains characterized by a missing or excess atom compared with the same-sized region in the perfect crystal so that such extended defects may be viewed as dropletlike regions of enhanced or diminished density. However, the implications of such a transformation, or whether it even occurs in crystalline Si, remain uncertain. To address this fundamental problem, we consider a comprehensive thermodynamic analysis of the thermodynamics of vacancy and self-interstitial formation over a broad $T$ range based on thermodynamic integration with a focus on entropic contributions. In cooled liquids, it is well known that the form of the intermolecular potential can greatly influence the configurational entropy $S_c$, and correspondingly, we analyze several empirical Si potentials to determine how the potential influences both the $T$ dependence of $S_c$ and the enthalpy and entropy of defect formation. We indeed find that the $S_c$ associated with point defects increases significantly upon heating, consistent with the existence of extended defects. Moreover, each type of defect species gives a significantly different contribution to $S_c$ at elevated $T$ and to a qualitive difference in the $T$ dependence of the entropy of defect formation in the extended defect regime. We discuss some potential consequences of these thermodynamic changes of defect formation on the $T$ dependence of diffusion in heated crystals.