Numerical simulation of vacuum dezincing of lead alloy

Removing zinc by distillation can leave the lead bullion virtually free of zinc and also produces pure zinc crystals. Batch distillation is considered in a hemispherical kettle with water-cooled lid, under high vacuum (50 Pa or less). Sufficient zinc concentration at the evaporating surface is achieved by means of a mechanical stirrer. The numerical model is based on the multiphysics simulation package PHYSICA. The fluid flow module of the code is used to simulate the action of the stirring impeller and to determine the temperature and concentration fields throughout the liquid volume including the evaporating surface. The rate of zinc evaporation and condensation is then modelled using Langmuir’s equations. Diffusion of the zinc vapour through the residual air in the vacuum gap is also taken into account. Computed results show that the mixing is sufficient and the rate-limiting step of the process is the surface evaporation driven by the difference of the equilibrium vapour pressure and the actual partial pressure of zinc vapour. However, at higher zinc concentrations, the heat transfer through the growing zinc crystal crust towards the cold steel lid may become the limiting factor because the crystallization front may reach the melting point. The computational model can be very useful in optimising the process within its safe limits.

A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data

The SB distributional model of Johnson's 1949 paper was introduced by a transformation to normality, that is, z ~ N(0, 1), consisting of a linear scaling to the range (0, 1), a logit transformation, and an affine transformation, z = γ + δu. The model, in its original parameterization, has often been used in forest diameter distribution modelling. In this paper, we define the SB distribution in terms of the inverse transformation from normality, including an initial linear scaling transformation, u = γ′ + δ′z (δ′ = 1/δ and γ′ = �γ/δ). The SB model in terms of the new parameterization is derived, and maximum likelihood estimation schema are presented for both model parameterizations. The statistical properties of the two alternative parameterizations are compared empirically on 20 data sets of diameter distributions of Changbai larch (Larix olgensis Henry). The new parameterization is shown to be statistically better than Johnson's original parameterization for the data sets considered here.

Reliability study of the electroless Ni–P layer against solder alloy

Copper (Cu) has been widely used in the under bump metallurgy of chip and substrate metallization for chip packaging. However, due to the rapid formation of Cu–Sn intermetallic compound (IMC) at the tin-based solder/Cu interface during solder reaction, the reliability of this type of solder joint is a serious concern. In this work, electroless nickel–phosphorous (Ni–P) layer was deposited on the Cu pad of the flexible substrate as a diffusion barrier between Cu and the solder materials. The deposition was carried out in a commercial acidic sodium hypophosphite bath at 85 °C for different pH values. It was found that for the same deposition time period, higher pH bath composition (mild acidic) yields thicker Ni–P layer with lower phosphorous content. Solder balls having composition 62%Sn–36%Pb–2%Ag were reflowed at 240 °C for 1 to 180 min on three types of electroless Ni–P layers deposited at the pH value of 4, 4.8 and 6, respectively. Thermal stability of the electroless Ni–P barrier layer against the Sn–36%Pb–2%Ag solder reflowed for different time periods was examined by scanning electron microscopy equipped with energy dispersed X-ray. Solder ball shear test was performed in order to find out the relationship between the mechanical strength of solder joints and the characteristics of the electroless Ni–P layer deposited. The layer deposited in the pH 4 acidic bath showed the weak barrier against reflow soldering whereas layer deposited in pH 6 acidic bath showed better barrier against reflow soldering. Mechanical strength of the joints were deteriorated quickly in the layer deposited at pH 4 acidic bath, which was found to be thin and has a high phosphorous content. From the cross-sectional studies and fracture surface analyses, it was found that the appearance of the dark crystalline phosphorous-rich Ni layer weakened the interface and hence lower solder ball shear strength. Ni–Sn IMC formed at the interfaces was found to be more stable at the low phosphorous content (∼14 at.%) layer. Electroless Ni–P deposited at mild acidic bath resulting phosphorous content of around 14 at.% is suggested as the best barrier layer for Sn–36%Pb–2%Ag solder.

The effects of thermo-electrically induced convection in alloy solidification

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using a 2-dimensional enthalpy based numerical model. Using an approximation of the dendrite growing in free space it was found that the resulting Lorentz force generates a circulating flow influencing the solidification pattern. As the magnetic field strength increases it was found that secondary growth on the clockwise side of the primary arm of the dendrite was encouraged, while the anticlockwise side is suppressed due to a reduction in local free energy. The preferred direction of growth rotated in the clockwise sense under an anti-clockwise flow for both the binary alloy and pure material. The tip velociy is significantly increased compared to growth in stagnant flow. This is due to a small recirculation that follows the tip of the dendrite; bringing in colder liquid and lower concentrations of solute. The recirculation being not normally incident on the tip is most likely the cause for the rotation. Grain growth consisting of multiple seeds with the same anisotropy growing in the same plane, gives a competition to release latent heat resulting in stunted growth. The initial growth for each dendrite is very similar to the single seed cases indicating that dendrites must become before the thermoelectric interactions are significant.

Thermoelectric effects on alloy solidification microstructure

Thermoelectric currents in the presence of a magnetic field generate Lorentz forces which can drive fluid flow. In the case of dendritic growth a naturally occurring thermoelectric current exists and in the presence of a high magnetic field micro convections are generated. Experimental evidence has attributed changes in microstructure to this effect. A numerical model has been developed to study the flow field around an unconstricted equiaxed dendrite growing under these conditions. The growth is modeled in 2D and 3D by an enthalpy based method and a complex flow structure has been predicted. Using a pseudo-3D approximation for economy, realistic 2D simulations are obtained where a fully coupled transient scheme reveals significant changes to the dendrite morphology reflecting experimental evidence. There is a rotation of the preferred direction of growth and increased secondary branching.

Modelling the tilt-casting process for the tranquil filling of titanium alloy turbine blades

The tilt-casting method is used to achieve tranquil filling of gamma-TiAl turbine blades. The reactive alloy is melted in a cold crucible using an induction coil and then the complete crucible-mould- running system assembly is rotated through 180degrees to transfer the metal into the mould. The induction current is ramped down gradually as the rotation starts and the mould is preheated to maintain superheat. The liquid metal then enters the mould and the gas within it (argon) escapes through the inlet aperture and through auxiliary vents. Solidification starts as soon the metal enters the mould and it is important to account for this effect to predict and prevent misruns. The rotation rate has to be controlled carefully to allow sufficient time for gas evacuation, but at the same time preserve superheat. This 3-phase system is modelled using the FV method, with a fast implicit numerical scheme used to capture the transient liquid free surface. The enthalpy method is used to model solidification and predict defects such as trapped bubbles, macro-porosity or surface connected porosity. Modeling is used to support an experimental program for the development of a production method for gamma-TiAl blades, with a target length of 40cm. The experiments provide validation for the model and the model in turn optimizes the tilt-casting process. The work is part of the EU project IMPRESS.