Determination of the melting and solidification characteristics of solders using differential scanning calorimetry

Differential scanning calorimetry (DSC) is used in the present study to determine the onset temperature of phase transformation and the enthalpy of fusion of various solder alloys. The solders studied are Sn-Pb, Sn-Bi, Ag-Sn, In-Ag, and Sn-Pb-Bi alloys. Very notable undercooling, such as 35 °C, is observed in the solidification process; however, a superheating effect is not as significant in the heating process. Besides the direct measurements of reaction temperature and heat of fusion, the fraction solid vs temperature has also been determined using a DSC coupled with a mathematical-model method. The heating and cooling curves of the solders are first determined using DSC. By mathematically modeling the heat transfer of the DSC cells, the heat evolution and absorption can be calculated, and then the melting and solidification curves of the solder alloys are determined. The three ternary alloys, Sn-35 wt pct Pb-10 wt pct Bi, Sn-45 wt pct Pb-10 wt pct Bi, and Sn-55 wt pct Pb-10 wt pct Bi, displayed similar DSC cooling curves, which had three reaction peaks. However, the solid fractions of the three alloys at the same temperature in the semisolid state, which had been determined quantitatively using the DSC coupled with a mathematical method, were different, and their primary solidification phases were also different.     

Macrosegregation during solidification resulting from density differences in the liquid

Macrosegregation has been observed in directionally solidified Pb-20 pct Sn alloys, over a range of freezing rates and temperature gradients. The macrosegregation was shown to result from the upward flow of less dense, tin rich, interdendritic liquid during solidification, using radioactive tracer techniques. For comparison, it was shown that macrosegregation occurred in the opposite direction in a Sn-4 pct Pb alloy, where the interdendritic liquid was lead rich, and consequently more dense. Shrinkage trails and pipes were observed in some of the Pb-20 pct Sn ingots, similar to “freckles” observed in directionally cast superalloys. A mathematical model for macrosegregation in vertically solidified ingots is presented, the driving force being the density differences in the interdendritic liquid during solidification. Liquid flow through the dendritic array is estimated by considering the partially solidified alloy as a porous medium of variable porosity. For simplicity, the model neglects backflow due to volume shrinkage (inverse segregation). The experimental results are compared to the model predictions. Formerly Research Associate, Department of Metallurgy, University of British Columbia     

Numerical simulation of macrosegregation: a comparison between finite volume method and finite element method predictions and a confrontation with experiments

Micro-macrosegregation calculations have been performed for a rectangular cavity containing either a Pb-48 wt pct Sn alloy or a Sn-5 wt pct Pb alloy. The numerical results calculated with a finite volume method (FVM) and a finite element method (FEM) are compared with experimental results previously obtained by Hebditch and Hunt. The two methods are based on the same average conservation equations governing heat and mass transfer and the same assumptions: lever rule, equal and constant density of the solid and liquid phases (except in the buoyancy term), permeability of the mushy zone given by the Carman-Kozeny relation, and no transport of the solid phase. Although the same parameters are used in both calculations, small differences are observed as a result of the different formulations. In particular, the instabilities appearing in the mushy zone (channels) of the Sn-5 wt pct Pb alloy are more pronounced with the FVM formulation as compared with FEM, whereas the opposite trend is observed for the Pb-48 wt pct Sn alloy. Nevertheless, the final segregation maps at the end of solidification compare fairly well with the experimental findings.     

Thermosolutal convection during dendritic solidification of alloys: Part II. Nonlinear convection

A mathematical model of thermosolutal convection in directionally solidified dendritic alloys has been developed that includes a mushy zone underlying an all-liquid region. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentrates that move upward at a constant solidification velocity. The initial state is perturbed, nonlinear calculations are performed to model convection of the liquid when the system is unstable, and the results are compared with the predictions of a linear stability analysis. The mushy zone is modeled as a porous medium of variable porosity consistent with the volume fraction of, interdendritic liquid that satisfies the conservation equations for energy and solute concentrations. Results are presented for systems involving lead-tin alloys (Pb-10 wt pct Sn and Pb-20 wt pct Sn) and show significant differences with results of plane-front solidification. The calculations show that convection in the mushy zone is mainly driven by convection in the all-liquid region, and convection of the interdendritic liquid is only significant in the upper 20 pct of the mushy zone if it is significant at all. The calculated results also show that the systems are stable at reduced gravity levels of the order of 10⁻⁴ g ₀ (g ₀=980 cm·s⁻¹) or when the lateral dimensions of the container are small enough, for stable temperature gradients between 2.5≤G _l≤100 K·cm⁻¹ at solidification velocities of 2 to 8 cm·h⁻¹.     

The solubility and solution behavior of antimony and tin in α-lron and the effects of nickel and chromium additions

The solid solubilities of Sn and Sb in α-Fe have been determined by means of lattice parameter measurements. The Sb solubility ranges from a maximum of 11 wt pct (5.4 at. pct) at 1000°C down to 5.3 wt pct (2.5 at. pet) at 600°C; the Sn solubility ranges from a maximum of 17.7 wt pct (9.2 at. pet) at 900°C to 6.5 wt pct (3.2 at. pet) at 600°C. These solubilities are remarkably large in view of the large sizes of the Sb and Sn atoms in relation to the Fe atom. It was not possible to rationalize the variation of the α-phase lattice parameter with Sb or Sn content from the point of view of atomic diameter or atomic volume. The addition of 1 wt pct Ni lowers the Sb solubility at 600°C from 5.3 to 3.5 wt pct (2.5 to 1.6 at. pet); the effect of Cr on the Sb solubility appears to be small. The addition of 1 wt pct Ni or 1 wt pct Cr lowers the Sn solubility from 6.5 to 5.2 wt pct (3.2 to 2.5 at. pet). It was found that a substantial amount of Ni substitutes for Fe in both the FeSb phase and the Fe₅Sn₃ phase. Formerly Research Fellow, Department of Metallurgy and Materials Science and LRSM, University of Pennsylvania     

Enthalpies of a binary alloy during solidification

The purpose of the paper is to present a method of calculating the enthalpy of a dendritic alloy during solidification. The enthalpies of the dendritic solid and interdendritic liquid of alloys of the Pb-Sn system are evaluated, but the method could be applied to other binaries, as well. The enthalpies are consistent with a recent evaluation of the thermodynamics of Pb-Sn alloys and with the redistribution of solute in the same during dendritic solidification. Because of the heat of mixing in Pb-Sn alloys, the interdendritic liquid of hypoeutectic alloys (Pb-rich) of less than 50 wt pct Sn has enthalpies that increase as temperature decreases during solidification. For some concentrations of Sn, the enthalpy of the dendritic solid at the solid-liquid interface also increases with decreasing temperature during solidification. Of particular concern, in formulating the energy equation, is the fact that the heat of fusion during solidification increases as much as 80 pct for hypoeutectic alloys and decreases as much as 25 pct for hypereutectic alloys. Thus the often applied assumptions of a constant specific heat and/or a constant heat of solidification could lead to errors in numerical modeling of temperature fields for dendritic solidification processes.     

An investigation of the high-temperature and solidification microstructures of PH 13-8 Mo stainless steel

Differential thermal analysis (DTA), high-temperature water-quench (WQ) experiments, and optical and electron microscopy were used to establish the near-solidus and solidification microstructures in PH 13-8 Mo. On heating at a rate of 0. 33 °C/s, this alloy begins to transform from austenite to δ-ferrite at ≈1350 °C. Transformation is complete by ≈1435 °C. The solidus is reached at ≈1447 °C, and the liquidus is ≈1493 °C. On cooling from the liquid state at a rate of 0. 33 °C/s, solidification is completed as δ-ferrite with subsequent transformation to austenite beginning in the solid state at ≈1364 °C. Insufficient time at temperature is available for complete transformation and the resulting room-temperature microstructure consists of matrix martensite (derived from the shear decomposition of the austenite) and residual δ-ferrite. The residual δ-ferrite in the DTA sample is enriched in Cr (≈16 wt pct), Mo (≈4 wt pct), and Al (≈1. 5 wt pct) and depleted in Ni (≈4 wt pct) relative to the martensite (≈12. 5 wt pct Cr, ≈2 wt pct Mo, ≈1 wt pct Al, ≈9 wt pct Ni). Solid-state transformation of δσ γ was found to be quench-rate sensitive with large grain, fully ferritic microstructures undergoing a massive transformation as a result of water quenching, while a diffusionally controlled Widmanstätten structure was produced in air-cooled samples.     

Efficient estimation of diffusion during dendritic solidification

A very efficient finite difference method has been developed to estimate the solute redistribution during solidification with diffusion in the solid. This method is validated by comparing our computed results to the results of an analytical solution derived by Kobayashi^[4] for the as-sumptions of a constant diffusion coefficient, a constant equilibrium partition ratio, and a par-abolic rate of the advancement of the solid/liquid interface. The flexibility of our method is demonstrated by applying it to the dendritic solidification of a Pb-15 wt pct Sn alloy, for which the equilibrium partition ratio and diffusion coefficient vary substantially during solidification. The fraction eutectic at the end of solidification is also obtained by estimating the fraction solid, in greater resolution, where the concentration of solute in the interdendritic liquid reaches the eutectic composition of the alloy. TURBO PASCAL is a trademark of Borland International, Scotts Valley, CA. IBM PC is a trademark of International Business Machines Corporation, Armonk, NY.     

The columnar to equiaxed transition in tin-lead alloys

Tin-lead alloys were solidified directionally and the position of the columnar to equiaxed transition determined on vertical sections of the ingots. The columnar length was found to increase with decreasing lead concentration and increasing heat transfer coefficient. A mathematical model of the heat flow in the system was used to determine local temperatures, temperature gradients, and velocities in the solidifying alloy. Comparing the position of the columnar to equiaxed transition and local thermal conditions, it was found that the transition occurred when the temperature gradient in the melt at the liquidus temperature was 0.11°C/mm for Sn 10 wt pct Pb, 0.10°C/mm for Sn 5 wt pct Pb, and 0.13°C/mm for Sn 15 wt pct Pb. The position of the transformation was found to be independent of melt superheat for the conditions considered.     

Phase equilibria for iron-rich Fe−Cu−C alloys: 1500 to 950°C

Isothermal sections for the iron rich corner of the Fe−Cu−C system have been constructed at 1500, 1450, 1200, 1172, 1150, 1000, and 950°C. A ternary invariant point exists at 1172°C where an iron rich liquid, a copper rich liquid, austenite, and graphite coexist. The iron rich liquid contains 3.7 wt pct Cu and 4.0 wt pct C. The austenite contains 7.3 pct Cu and 1.6 pct C. The copper rich liquid contains 2.4 pct Fe, and apparently very little carbon. The diagrams are used to explain the phenomena of “inverse segregation” that occurs during the solidification of iron rich Fe−Cu−C alloys. KRISHNA PARAMESWARAN, formerly Metallurgy Graduate Student, University of Missouri-Rolla KENNETH METZ, formerly Metallurgy Graduate Student, University of Missouri-Rolla     

Thermal analysis of the compositional shift in a transient liquid phase during sintering of a ternary Cu-Sn-Bi powder mixture

In this work, differential scanning calorimetry (DSC) and microstructural analysis were used to study the transient-liquid-phase sintering (TLPS) of a Cu-Sn-Bi powder mixture. During sintering, the liquid phase shifts from a Sn-rich (i.e., ∼90 wt pct Sn) to a Bi-rich (i.e., >78 wt pct Bi) composition. In addition, the presence of Bi creates two melting events: a Sn:Bi eutectic reaction at 139 °C and a reaction involving the melting of (Bi) at 191 °C. The Sn:Bi eutectic melting event was fully transient. The melting event at 191 °C was consistent with the formation of a terminal Bi-rich liquid phase. The rate of compositional shift toward this terminal liquid phase at 260 °C was dependent on the rate of the reaction of the Sn with the Cu powder to form intermetallic phases. For mixtures made with medium and fine Cu powder, the terminal Bi-rich composition was reached after isothermal hold times of 20 and 15 minutes, respectively. This resulted in a new melting point for the mixture of 191 °C. For coarse Cu powders, the rate of the compositional shift toward a Bi-rich composition was much slower. The liquid phase remained at a hypoeutectic Sn-Bi composition estimated at 80 wt pct Sn, while the mixture maintained a melting point of 139 °C.     

Application of MIVM for Pb-Sn System in Vacuum Distillation

The activity coefficients of components of the Pb-Sn binary alloy system were calculated based on the molecular interaction volume model (MIVM). A significant advantage of this model lies in its ability to predict the thermodynamic properties of liquid alloys using only two binary infinite activity coefficients. Based on the MIVM, the vapor-liquid phase equilibrium of the Pb-Sn alloy system in vacuum distillation has been predicted using the activity coefficients of Pb and Sn. The results showed that the content of tin in the vapor phase was 0.008?wt?pct, while in the liquid phase, it was 83?wt?pct at 1173?K (900?°C); it reached 0.022?wt?pct in the vapor phase, while in the liquid phase, it was 92?wt?pct at 1223?K (950?°C); and it was 0.052?wt?pct in the vapor phase, while in the liquid phase, it was 97.88?wt?pct at 1273?K (1000?°C). The content of tin in the vapor phase increased with the distillation temperature increasing. Experimental investigations into the separation of Pb and Sn from the Pb-Sn alloy by vacuum distillation were carried out for the proper interpretation of the results of the model. The influence of the distillation time (20 to 80?minutes) and the distillation temperatures of 1173?K, 1223?K, and 1273?K (900?°C, 950?°C, and 1000?°C) on the separating effect was also studied. The experimental results showed that the content of tin in the vapor phase was 0.085?wt?pct, while in liquid phase, it was 83?wt?pct under the operational conditions of distillation temperature of 1173?K (900?°C), evaporation time of 20?minutes, and chamber pressure of 20?Pa; it reached 0.18?wt?pct in the vapor phase, while in the liquid phase, it was 92?wt?pct at 1223?K (950?°C), 20?minutes, and 20?Pa; and it was 0.35?wt?pct in the vapor phase, while in the liquid phase, it was 97.88?wt?pct at 1273?K (1000?°C), 20?minutes, and 20?Pa. In all these experiments, it was observed that the content of tin in the vapor phase increased as the distillation time and temperatures were increased. The experimental results are in good agreement with the predicted values of the MIVM for the Pb-Sn binary system.     

Solidification of undercooled Sn-Sb peritectic alloys: Part I. Microstructural evolution

The droplet emulsion technique, which involves dispersal of a bulk liquid alloy into a collection of fine droplets (5 to 30μm), was applied to Sn-Sb alloys to yield high levels of controlled undercooling. The maximum undercooling levels achieved varied from 179 °C for pure Sn to 113 °C for a Sn-16 at. pct Sb alloy. Analysis of hypoperitectic alloy samples (alloys with an Sb content less than that of the liquid at the peritectic temperature) indicates that solute trapping occurs during solidification at the levels of undercooling and cooling rate investigated, yielding nearly homogeneousβ-tin solid solutions with compositions approaching those of the bulk alloys. With increasing undercooling and/or cooling rate, hyperperitectic alloys exhibit a transition from a highly segregated structure consisting of faceted primary intermetallic phase and cellularβ to a structure consisting primarily of a supersaturated tin-rich solid solution. Lattice constant measurements confirm that virtually complete supersaturation ofβ-tin was achieved in emulsion samples cooled at 200 °C s^s−1 for compositions up to approximately 20 at. pct Sb. The development and characteristics of subsequent solid-state precipitation were used to guide the interpretation of the often complex solidification reaction sequences in the hyperperitectic alloys. The formation of supersaturatedβ-tin solid solutions in the undercooled samples is related to the appropriate metastable phase equilibria and the development of solute trapping. Formerly Graduate Student, Department of Materials Science and Engineering, University of Wisconsin-Madison     

Heterogeneous nucleation of solidification of Si by solid AI in hypoeutectic Al-Si alloy

Melt-spun Al-3 wt pct Si with and without ternary additions of Na and Sr has been heat-treated above the Al-Si eutectic temperature in a differential scanning calorimeter to form a microstructure of Al-Si eutectic liquid droplets embedded in the α-Al matrix. During subsequent cooling in the calorimeter, the heterogeneous nucleation temperature for solidification of Si in contact with the surrounding Al matrix depends sensitively on the alloy purity, with a nucleation undercooling which increases with increasing alloy purity from 9 to 63 K below the Al-Si eutectic temperature. These results are consistent with Southin’s hypothesis that low levels of trace P impurities are effective in catalyzing Si nucleation in contact with the surrounding Al matrix. With a low Al purity alloy, 0.1 wt pct Na addition increases the Si nucleation undercooling from 9 to 50 K, 0.15 wt pct Sr addition does not affect the Si nucleation temperature, and 0.3 wt pct Sr addition decreases the Si nucleation undercooling from 9 to 3 to 4 K. The solidified microstructure of the liquid Al-Si eutectic droplets embedded in the Al matrix depends on the Si nucleation undercooling. With low Si nucleation undercooling, each Al-Si eutectic liquid droplet solidifies to form one faceted Si particle; however, with high Si nucleation undercooling, each Al-Si eutectic droplet solidifies to form a large number of nonfaceted Si particles embedded in Al. Formerly with the Oxford Centre for Advanced Materials and Composites, Department of Materials, Oxford University     

Equilibrium solid solubility of silicon in silver

The equilibrium solubility of silicon in silver was measured in the range between 300 °C and the eutectic temperature using both an electron microprobe and the evolution of electrical resistivity of a near-eutectic Ag-4 wt pct Si alloy. The silver matrix was found to dissolve up to 0.93 at. pct Si, at 836 °C. The resistivity was found to increase on average by 4.31 μΩcm/at. pct solute content of Si in the silver matrix. The solubility of silicon in silver is well described by an Arrhenius-type equation, with an apparent enthalpy of mixing of 74.7 kJ/mol and a prefactor of 30.6 (3060 at. pct). This finite terminal solubility of silicon in silver can account for a discrepancy between the calculated and experimental silver-silicon binary-phase diagrams, as present in the literature.     

On The Formation of Macrosegregations in

The effect of the natural convection on the formation of macrosegregations has been experimentally and theoretically analyzed. The Sn-10 pct Pb and Pb-15 pct Sn alloys were unidirectionally solidified. The temperature gradient and the solidification direction were perpendicular to the gravity vector. The concentration and temperature gradients in the samples cause natural con- vection. Large macrosegregations were observed in the sample. Two different convection modes were found in the two alloys caused by different density gradients in the two-phase region. This difference in convection causes an enrichment of Pb in the lower part of the last solidified regions in the Sn-10 pct Pb alloy and an enrichment of Sn in the upper part in the Pb-15 pct Sn alloy. Computer simulation of the convection mode models the convection pattern and the solidification process during which macrosegregation occurs. Formerly with the Department of Casting Formerly with the Department of Casting     

Microstructure Formation in a Gas-Atomized Drop of Al-Pb-Sn Immiscible Alloy

Al-Pb-Sn alloy is rapidly solidified by using the high-pressure gas-atomization technique. A model describing the microstructure evolution in an atomized drop is developed. This model takes into account the concurrent actions of the nucleation, diffusional growth, spatial motions of the minority-phase droplets, and the solidification of the matrix liquid. The microstructure formation in the gas-atomized drop is simulated by coupling the thermodynamic and kinetic calculations. The numerical results show a favorable agreement with the experimental results. They demonstrate that under the rapid cooling conditions of gas atomization, the spatial phase separation due to the Marangoni migration of the minority-phase droplets mainly affects the microstructure formation in a small region close to the atomized drop surface. All the minority-phase droplets are nucleated during the liquid?Cliquid phase decomposition period. For an Al-(5-9)?wt?pct Pb-3?wt?pct Sn alloy, the average radius and number density of the minority-phase particles depend exponentially on the powder diameter. The microstructure formation process is discussed in detail.     

The effect of low gold concentrations on the creep of eutectic tin-lead joints

The effects of low Au concentrations on the creep properties of a eutectic Sn/Pb alloy were investigated. Creep testing was performed on double-shear specimens of fine-grained, eutectic Sn/Pb joints with Au concentrations of 0, 0.2, 1.0, and 1.5 wt pct Au at 90 °C, 0, 0.2, and 1.0 wt pct Au at 65°C, and 0.2 wt pct Au at 25 °C. In the absence of Au, the creep of finegrained eutectic Sn/Pb is dominated by grain-boundary sliding at high homologous temperature and intermediate stress. The addition of 0.2 wt pct Au or more suppressed this mechanism; the high-stress, bulk-creep mechanism was dominant at all stresses tested. Higher concentrations of Au increased porosity within the joints. The porosity decreased joint strength. During failure, the crack path followed softer regions of the joint; cracks propagated through Pb-rich islands or along Sn/Sn grain boundaries.     

Effect of anthracite properties and formulation on properties of bench scale cathode blocks for aluminum smelting

Bench scale cathode blocks for aluminum smelting having an aggregate of 70 pct anthracite calcined at 1135°C—30 pct ball milled graphite and a coal tar pitch binder were fabricated, baked at 1135°C, and tested for electrical resistivity and expansion during electrolysis in a test cell. Twelve anthracite samples, for which a number of chemical and physical properties were determined, were used in cathode fabrication so that relationships among anthracite properties and cathode properties could be determined. Cathode expansion during electrolysis increased with increasing sulfur content of the anthracite but appeared to decrease with increasing silicon content. Electrical resistivity decreased with an increase in the fraction of green anthracite exhibiting a conchoidal rather than laminar fracture. With the finer of two anthracite aggregate sizings used, both cathode expansion during electrolysis and electrical resistivity decreased sharply as binder content was increased from 16 to 22 pct. Baked apparent density also increased at the same time but was not,per se, a valid indicator of either electrical resistivity or expansion during electrolysis; cathodes produced using a coarser anthracite sizing, which resulted in higher baked apparent densities, had higher electrical resistivities and expansions during electrolysis. Electrical resistance of all cathodes increased during electrolysis in the test cell by an amount proportional to the amount of expansion.     

Solidification Analysis of an Al-19 Pct Si Alloy Using <Emphasis Type="Italic">In-Situ</Emphasis> Neutron Diffraction

In-situ neutron diffraction and thermal analysis techniques were used simultaneously to evaluate the kinetics of the nonequilibrium solidification process of an Al-19 pct Si binary alloy. Feasibility studies concerning the application of neutron diffraction for advanced solidification analysis were undertaken to explore its potential for high resolution phase analysis coupled with fraction solid/liquid analysis of phase constituents. Neutron diffraction patterns were collected in a stepwise mode during solidification between 983 K and 793 K (710 °C and 520 °C). The variation of intensity of the diffraction peaks was analyzed and compared to the results of conventional cooling curve analysis. Neutron diffraction was capable of detecting nucleation of the Si phase (primary and eutectic), as well as the Al phase during Al-Si eutectic nucleation. Moreover, neutron diffraction indicated the possibility of detecting the presence of Si peaks at near liquidus temperature and premature nucleation of α-Al prior to Al-Si eutectic temperature. The solid and liquid volume fractions were determined based on the change of intensity of neutron diffraction peaks over the solidification interval. Overall, the volume fraction determined was in good agreement with the results of the cooling curve thermal analysis, as well as calculations using the FactSage software. The potential of neutron diffraction for high resolution melt analysis required for advanced studies of grain refining, eutectic modification, etc. was illustrated. This study will help us better understand the solidification mechanism of Al-Si alloys used for various casting component applications.