Solidification Of Tin Research Articles

3D numerical simulation and experimental investigation of pure tin solidification under natural and forced convection

The numerical simulation of the horizontal solidification of pure tin under natural convection and under forced convection induced by Electromagnetic Stirring (EMS) is presented and compared with experimental results obtained by the ‘AFRODITE’ benchmark setup, described in several previous publications [6–10]. The experiment consists in solidifying a rectangular ingot (100 × 10 × 60 mm) using two lateral heat exchangers which allow the application of a controlled horizontal temperature difference. The experimental temperature difference between the two lateral sides of the sample DT = 40 K and the cooling rate CR = −0.03K/s. Under these conditions the solidification front is planar throughout the experiment. Enthalpy formulation based on fixed-grid techniques is used for the numerical simulations of the phase-change problems, accounting for buoyancy convection and forced convection created by Lorentz forces generated by an external Traveling Magnetic Field (TMF). The temperature distribution obtained by numerical simulation is demonstrated to effectively reproduce the temperature maps obtained from the experimental measurements. The proposed 3D numerical model has demonstrated its effectiveness in predicting the effect of EM stirring on the solidification process in terms of thermal field, dynamic field and the shape and localization of the solidification front.

A 2D1/2 model for natural convection and solidification in a narrow enclosure

Efficient numerical models are derived for problems of natural convection and material solidification in a horizontal differentially heated slender cavity. These 2D1/2 models are obtained by averaging the equations of momentum, heat, and mass conservation along the transverse direction assuming both a constant temperature and a well defined velocity profile in this direction. Based on our former works, the transverse velocity profile is assumed to be either a Poiseuille profile (2Dp1/2 model), or Hartmann-type profiles featuring two boundary layers on the sides of a uniform bulk (2DH1/2 model). For this 2DH1/2 model, however, a parameter δ (giving the boundary layer thickness) has to be adjusted: optimal values have been found in a large range of the control parameters and expressed as a reliable fitted function of Gr. The ability of the model to reproduce 3D results in a 2D framework is investigated in a large range of the control parameters (Prandtl number Pr and Grashof number Gr); the validity domain of the model in this parameter space is also clarified and rigorously defined. A good precision is obtained for natural convection problems (intensity of the flow, temperature field) as well as for solid-liquid phase change problems (shape, position, and evolution of the front). A comparison with unpublished experimental data of solidification of pure tin is also conducted. The boundary conditions for the simulation are first defined after a post-treatment of the time-dependent experimental data in order for them to be representative of the experimental process despite a significant and time dependent thermal resistance between the walls of the crucible and the liquid. A very good agreement is observed between the 2DH1/2 model and the experimental measurements for this pure tin solidification experiment in the AFRODITE setup.

Effect of Melt Superheating Treatment on the Latent Heat Release of Sn

The accuracy of the baseline evaluation is of importance for calculating the transition enthalpy such as the latent heat of the crystallization. This study demonstrates the modified method of the equivalent non-latent heat baseline, by which the transition enthalpy can be measured accurately according to the transition peak in differential scanning calorimetric curve. With this method, the effect of melt superheating treatment time on the latent heat release upon the solidification of tin is investigated. The results show that the latent heat increases by increasing the treatment time, and is close to a constant when the treatment time is large enough, indicating the homogeneous system. And then, a simple model is established to describe the changes of the crystallization latent heat with the treatment time, which is confirmed by the experimental data of Sn.

The Contribution of Constitutional Supercooling to Nucleation and Grain Formation

The concept of constitutional supercooling (CS) including the term itself was first described and discussed qualitatively by Rutter and Chalmers in order to understand the formation of cellular structures during the solidification of tin, and then quantified by Tiller et al. On that basis, Winegard and Chalmers further considered ‘supercooling and dendritic freezing of alloys’ where they described how CS promotes the heterogeneous nucleation of new crystals and the formation of an equiaxed zone. Since then the importance of CS in promoting the formation of equiaxed microstructures in both grain refined and unrefined alloys has been clearly revealed and quantified. This paper describes our current understanding of the role of CS in promoting nucleation and grain formation. It also highlights that CS, on the one hand, develops a nucleation-free zone surrounding each nucleated and growing grain and, on the other hand, protects this grain from readily remelting when temperature fluctuations occur due to convection. Further, due to the importance of the diffusion field that generates CS, recent analytical models are evaluated and compared with a numerical model. A comprehensive description of the mechanisms affecting nucleation and grain formation and the prediction of grain size is presented with reference to the influence of the casting conditions applied during the practical casting of an alloy.

Possibility of a shape phase transition for solidification of tin at scallop-like surfaces of Cu6Sn5

The possibility of solder-spreading transitions in solidification of solder at a rough rigid intermetallic surface is proven theoretically. Depending on the misorientation of scallops on the interface, one can observe a two-dimensional spreading transition over the scallops or a one-dimensional spreading transition along the triple-junction of two intermetallic compound scallops and liquid solder. The extent of undercooling can be determined not only by different interface energies, but by different angles between neighbouring scallops as well.

Solidification of tin on quasicrystalline surfaces

A two-phase alloy of β-Sn and Al63Cu25Fe12 quasicrystal produced by melt-spinning was annealed and aged to form various microstructures of tin in a quasicrystalline (QC) or microcrystalline (MC) matrix. The morphology and structure of the interfaces was studied by scanning and transmission electron microscopy and was related to melting and solidification behavior of tin studied by differential scanning calorimetry. In a MC matrix the tin phase occurred as nanoparticles and solidified with an undercooling of about 35°C. In a QC matrix, tin formed intergranular layers on faceted matrix grains. Tin showed multiple solidification peaks in undercooling ranging from 8°C to 43°C, indicating several distinct nucleation sites which compete with each other and are selected kinetically. The interfacial energy (depending on the structural state of the matrix) had a more dominating effect on the solidification of tin than the size, shape and the distribution of the tin particles. It was also concluded that solidification of tin is easier on quasicrystalline surfaces than on aluminum.

Validation of a 3D multi-physics model for unidirectional silicon solidification

A model for transient movements of solidification fronts has been added to X-stream, an existing multi-physics simulation program for high temperature processes with flow and chemical reactions. The implementation uses an enthalpy formulation and works on fixed grids. First we show the results of a 2D tin solidification benchmark case, which allows a comparison of X-stream to two other codes and to measurements. Second, a complete 3D solar silicon Heat Exchange Method (HEM) furnace, as built by PVA TePla is modeled. Here, it was necessary to model the complete geometry including the quartz crucible, radiative heaters, bottom cooling, inert flushing gas, etc. For one specific recipe of the transient heater power steering, PVA TePla conducted dip-rod measurements of the silicon solidification front position as function of time. This yields a validation of the model when applied to a real life industrial crystallization process. The results indicate that melt convection does influence the energy distribution up to the start of crystallization at the crucible bottom. But from that point on, the release of latent heat seems to dominate the solidification process, and convection in the melt does not significantly influence the transient front shape.

Microstructure and In Situ Observations of Undercooling for Nucleation of β-Sn Relevant to Lead-Free Solder Alloys

Difficult nucleation of β-Sn during solidification of tin and tin-based lead-free solder alloys can result in high degrees of undercooling of the liquid prior to solidification. The undercooling can produce solder joints with large grains, anisotropic behavior, and undesirable mechanical properties. This paper describes our examination of the amount of undercooling of tin on both graphite (non-wetting) and copper (wetting) surfaces using in situ x-ray diffraction. The microstructure was further characterized by optical microscopy, scanning electron microscopy, and electron backscattering diffraction imaging microscopy. Undercoolings as high as 61°C were observed for Sn solidified on graphite, while lower undercoolings, up to 30°C, were observed for Sn solidified on copper. The microstructure of the high purity Sn sample solidified on graphite showed very few grains in the cross-section, while the commercially pure Sn sample solidified with only one grain and was twinned. Tin solidified on copper contained significant amounts of copper in the tin, intermetallic phase formation at the interface, and a eutectic microstructure.

An investigation of the influence of natural convection on tin solidification using a quasi two-dimensional experimental benchmark

A well validated, quasi two-dimensional, unsteady solidification experimental benchmark is proposed to study the critical role of thermally driven natural convection using commercial pure tin. The experiment consists of solidifying a parallelipedic sample from two vertical sidewalls using two heat exchangers in a rectangular cavity. The mean temperature gradient G T , and the mean cooling rate C R , are set to control the experimental process. An array of 50 thermocouples allows us to measure the instantaneous temperature field and its evolution. While in the liquid state, the isotherms exhibit a plausible convective heat flow and its intensity increases as the Rayleigh number increases. In the solidification process, a novel recalescence phenomenon is observed by tracing the solidifying front in a relatively slow cooling rate case. By setting different mean temperature gradients, different patterns of the natural convection and the temperature field evolutions are obtained. A discussion is also presented regarding the crystallography.

Interfacial reactions of Sn-Ag-Cu solders modified by minor Zn alloying addition

The near-ternary eutectic Sn-Ag-Cu alloys have been identified as leading Pb-free solder candidates to replace Pb-bearing solders in microelectronic applications. However, recent investigations on the processing behavior and solder joints reliability assessment have revealed several potential reliability risk factors associated with the alloy system. The formation of large Ag3Sn plates in Sn-Ag-Cu joints, especially when solidified in a relatively slow cooling rate, is one issue of concern. The implications of large Ag3Sn plates on solder joint performance and several methods to control them have been discussed in previous studies. The minor Zn addition was found to be effective in reducing the amount of undercooling required for tin solidification and thereby to suppress the formation of large Ag3Sn plates. The Zn addition also caused the changes in the bulk microstructure as well as the interfacial reaction. In this paper, an in-depth characterization of the interfacial reaction of Zn-added Sn-Ag-Cu solders on Cu and Au/Ni(P) surface finishes is reported. The effects of a Zn addition on modification of the interfacial IMCs and their growth kinetics are also discussed.

XRD and XPS study on reactive plasma sprayed titanium–titanium nitride coatings

Reactive plasma spraying of titanium in a nitrogen-containing plasma gas allows the formation of hard titanium composite coatings reinforced by in situ formed titanium nitrides (TiN and Ti 2N). In the present study, the formation of titanium nitrides during the reactive spraying of titanium was studied by means of two different analysis techniques: X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The diffusion and solidification sequence predicted by the Ti-N phase diagram was consistent with the experimental results. The nitrogen retained in the coating was found mainly as titanium nitrides and not as interstitial nitrogen in the titanium lattice. It is hypothesised that the formation and direct solidification of TiN occurs during the flight of the sprayed particles. The presence of solid TiN constrains the thermal contraction of titanium splats upon solidification. The observed cell distortion of the residual α-Ti is thus attributed to tensile stresses arising from the solidification process.

Thermal Behavior in Unidirectional Cooling of Some Materials under Microgravity

The overall heat transfer coefficients during solidification of tin are evaluated by unidirectional solidification under two conditions of 1G and microgravity of 10 -4 G. The heat transfer coefficient under microgravity reduces to about 60% compared with that obtained under the condition of usual gravity. This may be due to reduced contact pressure and hydrostatic pressure of tin in microgravity. Thermal convection flow of water and mercury are also investigated in a transition period from gravitational to microgravitational environments in order to recognize the effect of the convection flow on unidirectional solidification in the transition. Experiments in the microgravity environment were conducted in the facilities of a drop shaft located at Kamisunagawa in Japan (JAMIC).

Estimation of thermal contract resistance during the first stages of metal solidification process: II—experimental setup and results

This paper presents an experimental study of transient heat transfer in the early stages of solidification of some pure metals on water cooled substrate, quantified in terms of two parameters: thermal contact resistance at the interface and heat flux. Experiments were performed to measure the thermal contact resistance during solidification of tin, lead and zinc drop on nickel substrate. The study is focused on the heat transfer aspects of this process and the identification of parameters affecting the heat transfer mechanism. To this end, the influence of casting process variables such as substrate surface roughness, casting material, metal superheat and lubricant on heat transfer has been analyzed.

Solidification of tin droplets embedded in an aluminium matrix

The solidification behaviour of tin droplets embedded in an aluminium matrix in a rapidly solidified Al-5 wt % Sn alloy has been investigated by a combination of transmission electron microscopy and differential scanning calorimetry. Detailed transmission electron microscopy shows that rapidly solidified Al-5 wt % Sn consists of about 5 μm diameter columnar aluminium grains, with a fine-scale distribution of 20–300 nm sized tin particles embedded within the aluminium grains, and 100–400 nm sized tin particles at the aluminium grain boundaries. The tin particles exhibit two different orientation relationships with the aluminium matrix and a variety of different faceted shapes: {1 1 1}Al∥{1 0 0}Sn and 〈¯2 1 1〉Al∥〈0 1 0〉Sn, with the main facet parallel to {1 1 1}Al, and {1 0 0}Sn; and {1 0 0}Al∥{1 0 0}Sn and 〈0 1 1〉Al∥〈0 1 1〉Sn, with the main facet parallel to {1 0 0}Al and {1 0 0}Sn.In situ heating in the transmission electron microscope shows that the different tin particle shapes are not affected by heat treatment in the solid state, but change into a truncated octahedral shape bounded by {1 1 1}Al and {1 0 0}Al facets when the tin particles melt. The {1 0 0}Al-liquid Sn interfacial energy is about 9% larger than the {1 1 1}Al-liquid Sn interfacial energy just above the tin particle melting point, and the {1 0 0}Al/{1 1 1}Al interfacial energy anisotropy decreases gradually as the temperature increases above the melting point. Differential scanning calorimeter experiments show that the liquid tin droplets solidify in three stages. Firstly, the larger tin droplets at the aluminium grain boundaries solidify by nucleation on catalytic trace impurities, over a temperature range of 170–140 °C. Secondly and thirdly, the smaller tin particles embedded within the aluminium grains solidify by catalytic nucleation on the {1 0 0}Al and {1 1 1}Al facets, over the two temperature ranges of 140–128 °C and 128-115°C. Catalytic nucleation of the solidification of tin takes place at special sites such as steps or dislocations on the {1 0 0}Al and {1 1 1}Al facets with contact angles of 55° and 59°.

Numerical simulation of tin solidification under the influence of natural convection in a thick walled annular crucible

The freezing of pure tin in a thick-walled annular crucible under the influence of laminar thermal bouyancy and thermocapillary convection is numerically investigated. The problem analyzed is conjugate and incorporates both a free surface and moving phase front. A two-dimensional dynamic model is implemented using a previously proposed fixed-grid enthalpy based formulation in which the coupled momentum and energy equations are solved in their primitive variable form. The problem examined here includes important extensions to problems formerly used for verification of this method. Good agreement exists between numerically predicted solidification fronts and those experimentally determined by prior investigators.

Effects of a forced couette flow during the controlled solidification of a pure metal

The role of mixed convection, caused by a forced Couette flow, during the directional solidification of tin in a toroidal mould is studied. The macrostructure of the solidified melt is examined and the metallurgical findings (crystal growth) connected with the heat and fluid flow measurements. The results are compared with those obtained with another type of rotating flow, driven by a stationary electromagnetic field and produced by an annular electromagnetic conduction pump. The angle of deflection of the columnar crystals is related to the mean velocity and the shear stress upon the melt-solid interface, as well as to the initial superheat.

Effects of magnetically damped convection during the controlled solidification of metals and alloys

The role of natural and damped convection during the thermally controlled solidification of tin and aluminium alloys in a toroidal mould was studied. The damped convection was caused by a stationary and uniform magnetic field parallel to the gravity field. Temperature measurements made it possible to follow both the evolution of the solidification front and that of the temperature distribution inside the bulk liquid with time. These experiments were performed from various degrees of superheat, in the absence and presence of a magnetic field. A discussion is presented relating the crystallographical findings to the temperature field patterns.

Solidification of tin in the presence of electric and magnetic fields

The role of natural, damped and forced convection during the thermally controlled solidification of tin in a toroidal mould was studied. The damped convection was caused by a stationary magnetic field parallel to the gravity field, while the forced convection was provoked by an annular electromagnetic pump. Temperature measurements made it possible to follow both evolution of the solidification front and of the temperature distribution inside the bulk liquid with time. These experiments were performed from various degrees of superheating in the absence and presence of electric and magnetic fields. A discussion is presented relating the crystallographical findings to the thermal and fluid flow measurements.

Effects of electromagnetic stirring during the controlled solidification of tin

The role of natural and forced convections during solidification of pure tin in an annular crucible was studied. The forced convection was generated by electromagnetic stirring. Maps of electromagnetic body forces and velocity fields were obtained for various stirring intensities and various positions of the solidification front. Temperature measurements made it possible to follow the evolution of the solidification front with time. These experiments were carried out from various degrees of superheat both in the absence and presence of electromagnetic stirring. A discussion is presented relating the metallurgical findings (macrostructure) to the heat and fluid flow measurements.

Special government etalon of the brightness energy unit at the temperature of tin solidification

The special government etalon of the brightness energy unit at the tin solidification temperature, created in VNIIM, assures the reproduction of the unit and transmission of its dimension in conformity with the all-union checking scheme, by using working etalons and standard measurement facilities, to the working measurement facilities used in the national economy.