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The purpose of this paper is to investigate the influence of In additions on the wetting properties of the Sn2.86Ag0.40Cu (in wt%) eutectic‐based alloys, on a copper substrate, in the presence of a flux. The main goal was to find correlations between the results of the wetting balance (WB) and the sessile drop (SD) method, in relation to the contact angles.

The WB method was applied for the wetting measurements, at 250°C, in an air atmosphere and in the presence of a flux. The SD measurements were conducted at the same temperature, in the presence of the same flux, but in an Ar atmosphere, while the maximum bubble pressure (MBP) and dilatometric measurements were conducted in an Ar+H₂ atmosphere. The density data from the dilatometric method were used for the determination of the surface tension by means of MBP, and the WB method was used to determine the surface and interfacial tension. Next, the surface tension data from these two methods were compared. The WB data were used to calculate the contact angles and the obtained indirect data were compared with the results of the direct SD measurements of the contact angle.

A higher In content in the alloy resulted in a lower contact angle on the copper, and the WB results agreed well with the results of the SD experiments. It was confirmed that, in liquid In‐Sn and the alloys containing In and Sn (Ag‐In‐Sn, Sn‐Ag‐Cu‐In, Sn‐Zn‐In), the improvement of the wettability was indicated only by the increase of the contact angle with the increasing In content.

Further studies are necessary for the confirmation of practical application, but they should be directed to the soldering of high indium alloys on printed circuit boards, with different finishes and qualities of the solder joint performance.

Taking into account the contact angle data from the WB and SD methods, the best results of the SAC‐In alloy on copper were obtained for the alloy of the highest In content. It was found that the contact angles from SD after 4 s were higher (non‐equilibrium conditions) than the values calculated from WB after 3 s. In contrast, the contact angles from SD after 10 min (equilibrium conditions) were lower than those from WB after 3 s. The comparison suggests that the contact angles from WB are situated within the data from SD, showing the same lowering tendency with the increasing content of In, and they may be well accepted for practical purposes. On the other hand, the sample of the solder in the SD method, after a prolonged time – in order to get the equilibrium contact angle – may be used to study the interfacial phenomena with the Cu substrate. The differential thermal analysis results indicate that the melting temperature decreases with increasing tin concentration. Taking into account the results of this study and the available literature data, alloys containing 8‐10 wt% of In can be recommended for practical application.

The WB and SD methods were used for the contact angle determination of a wide range of solder compositions, in the same temperature and flux conditions. Also, the surface tensions for these alloys were determined with the use of two independent methods: the MBP and the WB methods. The results obtained made it possible to draw conclusions regarding the correlation between the output of different methods and the conditions in which a comparison of the results can be made. It is supposed that these observations apply to many other alloy systems.

The purpose of Part I of this paper is to investigate the influence of Bi additions on the surface tension, the interfacial tension, and the density of SnZn7Bi alloys (Bi=1 and 3 percent by mass) as a continuation of similar previous studies on Bi and Sb additions to the binary Sn‐Zn alloy. The main aim of Part I is to indicate that the lowering of the surface tension and interfacial tension is not sufficient for practical applications. However, knowledge of the interfacial tension between the soldering flux and the solder is necessary to convert the wetting force into the contact angle. This will be documented in Part II.

The maximum bubble method was applied for the surface tension and the Miyazaki method was applied for the surface tension and the interfacial tension, using the density values from the dilatometric technique. The experimental surface tension results are compared with the Butler's thermodynamic modeling results and are discussed by means of the analysis of variance (ANOVA).

On the basis of previous studies on Sn‐Zn‐Bi‐Sb alloys, the addition of Bi to SnZn7 slightly decreased the surface tension measured in an Ar+H₂ atmosphere, similarly to the Butler's modeling results. Also, a similar slight decrease of the surface tension from the Miyazaki method measured in air and in nitrogen was observed, as well as a more significant lowering of the interfacial tension with the use of a flux in nitrogen. There was also a slight influence of the temperature on the numerical values of the surface tensions and the interfacial tension. In the ANOVA, taking into account the Bi content, the temperature of measurements, the atmosphere and the flux, the flux used was shown as the most important, and also, to a lesser extent, the atmosphere.

It is intended (the purpose of Part II of this paper) to verify the positive influence of Bi additions in SnZn7 alloys on the surface tensions and the interfacial tensions via the contact angles from the interaction with Cu on printed circuit board with different lead‐free finishes.

It is suggested that further studies on more efficient fluxes are necessary for the practical application being in agreement with the ANOVA and the literature information.

A slight improvement of the wettability with the use of Bi additions in the SnZn7Bi alloys in the course of various experimental techniques is proven, similar to results reported in various references. The obtained results will enlarge the SURDAT database of lead‐free soldering materials.

The purpose of this paper is a comparable evaluation of the influence of a particular element (Bi and Sb) added to Sn‐Ag‐Cu and Sn‐Zn alloys on their surface and interfacial tensions, as well as the wetting properties on the Cu substrate expressed by the wetting angle.

The authors applied the L₈ orthogonal Taguchi array to carry out the experiments and discussed the results using analysis of variance (ANOVA).

It was expected, on the base of previous studies, the decrease of the surface and interfacial tensions and thus improving wettability after the Bi and Sb addition to Sn‐Ag‐Cu and Sn‐Zn alloys. Unfortunately, the obtained results on the quinary Sn‐Ag‐Cu‐Bi‐Sb alloys and the quaternary Sn‐Zn‐Bi‐Sb alloys do not confirm these trends. The performed analyses suggest that the compositions of the quinary Sn‐Ag‐Cu‐Bi‐Sb alloys, as well as the quaternary Sn‐Zn‐Bi‐Sb alloys, do not have optimal compositions for practical application. The Cu, Bi and Sb elements in the case of the Sn‐Ag‐Cu‐Bi‐Sb alloys and the Zn, Bi and Sb elements in the case of the Sn‐Zn‐Bi‐Sb alloys show mutual interaction and, in consequence, there is no correlation between the tendency of the surface and interfacial tensions changes and the wettings of the Cu substrate.

It is suggested that further studies are necessary for the purpose of the practical application, but they should be limited mainly to the Sn‐Ag‐Cu‐Bi and the Sn‐Zn‐Bi alloys with the optimal compositions.

The performed analysis suggests that none of the investigated compositions of the quinary Sn‐Ag‐Cu‐Bi‐Sb alloys, as well as the quaternary Sn‐Zn‐Bi‐Sb alloys, have the optimal compositions for practical application.

The quickest way to determine which element of the alloy composition influences the surface tension and the wetting properties, and how, is to apply orthogonal analysis. After choosing the orthogonal array, the experiments were performed and analysis of variance (ANOVA) was used to perform the quantifiable analysis of the measured and calculated results of surface and interfacial tensions, as well as the wetting properties on the Cu substrate.

The purpose of this paper is to investigate the influence of Bi additions on the wetting properties of SnZn7Bi alloys (Bi=1 and 3 per cent by mass) on a copper substrate and printed circuit boards (PCBs) with lead‐free finishes (SnCu, immersion Sn, Ni/Au, organic solderability preservative) in the presence of fluxes. The practical implications of the results is the main purpose of these investigations.

A wetting balance method was used for wetting measurements at 230 and 250°C in nitrogen and air atmospheres in the presence of ORM0‐ or ROL0‐type fluxes. The PCBs were investigated ‘as received’ and after accelerated aging. The analysis of variance (ANOVA) analysis was performed in order to explain how the main factors of the experiments (the Bi content in the alloy (1 or 3 per cent), the test temperature and the test atmosphere) influenced the wetting ability of SnZn7Bi on Cu substrates.

As expected, a higher temperature and a higher Bi content in the alloy favoured the wetting of the copper substrate in the presence of the ORM0‐type flux in a nitrogen atmosphere. These results were confirmed by ANOVA analysis. Very good results were also obtained for the SnZn7Bi3 alloy's wettability on “tin coatings” on PCBs (SnCu and immersion Sn) both “as received” and after aging, in the presence of the ORM0‐type flux, for all the applied testing conditions (in both temperatures and N₂ and air atmospheres). The less active flux (ROL0) caused a worsening of the alloy's wettability properties; however, the PCBs with SnCu and immersion Sn finishes maintained their wettability, even after aging, at very good and good levels, respectively.

It is suggested that further studies are necessary for confirmation of the practical application, but they should be limited to the soldering of SnZnBi3 on PCBs with “tin coatings” and the quality of the solder joint performance.

The best SnZn7Bi3 wetting results on PCBs with “tin coatings” (SnCu and immersion Sn) at 230 and 250°C and in N₂ and air atmospheres suggest the possibility of a practical usage of the tin‐zinc‐bismuth alloys for soldering in electronics using both the ORM0‐type flux and the even less active ROL0‐type flux, which are currently used in industrial lead‐free soldering processes.

The wetting balance method, combined with ANOVA was used as the quickest way to determine the wettability properties of SnZn7Bi on Cu substrates. Wettability measurements were also performed on the SnZn7 and SnZn7Bi alloys with different lead‐free finishes, in different experimental conditions.

Because of the complexity of relationship between surface tension and its decisive factors, such as temperature, concentration, electronic density, molar atomic volume and electro-negativity, a reasonable predicting model of surface tension of Sn-based solder alloys has not been developed yet. The paper aims to address the surface tension issue that has to be considered if the new lead free solder will be applied for electronics.

Using an artificial neural network (ANN) model with back-propagation (BP) algorithm, the surface tension for Sn-based binary solder alloys was simulated, and the comparison between the simulating results and data from experiments and literatures was analyzed as well. In addition, the relationship between surface tension and its decisive factors would be discussed based on the ANN and orthogonal design methods.

It is shown that the predicting model of surface tension of Sn-based solder alloys is constructed according to the BP–ANN theory, and the predicted value from the BP–ANN is in excellent agreement with the experimental results. The surface tension of Sn-based solders is determined by five factors, i.e. temperature, concentration, electronic density, molar atomic volume and electro-negativity. Among of the factors, molar atomic volume is major factor, and the order of degree of influence on surface tension is molar atomic volume > electro-negativity > electronic > density > concentration > temperature. Moreover, a simply reasonable equation is proposed to estimate the surface tension for Sn-based solders.

The five decisive factors of surface tension for Sn-based binary solder alloys have been analyzed theoretically, and a reasonable model of surface tension for Sn-based binary solder alloys is proposed as well. It is shown that ANN theory will be applied well to simulate the surface tension of Sn-based lead free solder.

The purpose of this article is to establish why the wetting on PCBs with SnCu (HASL) and Snimm finishes in the presence of a flux is better than the wetting of those on a copper substrate. The practical aspect of the obtained results is the main goal of these investigations.

The authors applied the wetting balance method for the wetting measurements at 230 and 250°C, in nitrogen atmosphere, in the presence of the ORM0 type flux. The PCBs with the SnCu (HASL) and Snimm finishes were investigated in the state “as received”. To establish the wetting properties of the SnCu (HASL) and Snimm finishes on the PCBs, wetted by the investigated SnZnBiIn alloys, the SEM and EDX analyses were performed.

The authors obtained very good wetting results of the PCBs with the SnCu and Snimm finishes, wetted by the SnZn7Bi3In4 alloys. By applying the SEM and EDX methods, it was possible to establish that the barrier layer which was created during the HASL process between the copper and the SnCu solder is efficient enough to protect the copper against the influence of the Zn atoms from the SnZn7Bi3In4 solder. This is the reason for an improvement of the wetting properties. An immersion tin finish does not create such barrier layer with the copper. It results in a worse wetting than for the SnCu finishes but a better one than that for the copper. Immersion tin dissolves in the alloys during the soldering and this process delays the reaction between the copper and the Zn atoms from the SnZn7Bi3In4 solder.

It is suggested that further studies are necessary for the confirmation of the practical application, but they should be limited to the reliability of the solder joint performance.

The best wetting results of the PCBs with “tin finishes”, especially with SnCu, wetted by the SnZn7Bi3In4 alloy, at 230 and 250°C and in nitrogen atmosphere, suggest a possibility of a practical usage of the tin‐zinc‐bismuth‐indium alloys for soldering in electronics.

The wetting balance method combined with the SEM and EDX analyses were used as the quickest way to determine the mechanism of the better wettability properties in the case of the PCBs with the SnCu and Snimm finishes, wetted by the SnZn7Bi3In4 alloy, compared to those of the PCBs on the Cu substrate.

The purpose of this paper is to study the effect of copper concentration in near‐eutectic liquid SAC solders on their thermophysical properties: viscosity, surface tension, density; as well as wetting behavior on copper substrates at 523 K.

Viscosity, surface tension, and density were studied over a broad range of temperatures with the recently developed Roach‐Henein method. The obtained results were compared with the data from modified capillary, maximum bubble pressure, wetting balance and dilatometric measurements. Wetting angles measured with wetting balance method were compared with the results of sessile drop measurements.

The results obtained indicate that increasing concentration of copper in the alloy results in higher density, surface tension and viscosity, but differences resulting from copper concentration on wettability are relatively small. At 523 K, the density is: 7.097, 7.186, 7.232 g cm⁻³, the surface tension is: 538.1, 553.5, 556.7 m Nm⁻¹, the viscosity is: 2.173, 2.227, 2.467 mPas, respectively, for alloys containing 0.41, 1.01 and 1.61 wt% of Cu. Wetting angles on copper substrates are similar within a margin of error for all compositions. The results of present study are compared with the available literature data and a relatively good agreement is observed.

This paper provides the data of thermophysical properties of widely‐used SAC solders including viscosity, of which there is little data in the literature. It is confirmed that the increased copper concentration increases viscosity, yet this effect is small and does not correlate with the wetting behavior.

The purpose of this paper is to investigate the influence of silver nanoparticle additions on the wetting properties of Sn‐Ag‐Cu (SAC) solder paste. In this investigation, the basic solder paste contained 85 wt.% of commercial Sn 96.5 Ag 3 Cu 0.5 powder (with the particle sizes in the range of 20‐38 μm) and 15 wt.% of self‐prepared middle activated rosin flux. To this paste was added 0.5, 1, 2 and 4 wt.% of self‐prepared silver nano‐powders of different grain sizes (from 9 to 138 nm). After the pastes had stabilized, their wetting properties were tested. The main goal of these investigations was to improve the wetting properties of SAC solder paste and to find correlations between the results of the wetting of solder paste with nanoparticles on the copper substrate with the microstructure of the solder joints.

The following methods were applied for the wetting solder paste investigation: spreading on the copper substrate, contact angle measurement on the copper and wetting on a FR‐4 laminate double sided with an 18‐μm thick copper foil. The investigations were performed at temperatures of 220, 230, 240 and 250°C. Cross‐sectioning was performed on the solder paste after reflow on the copper substrate. For the microstructural analysis of the “nano” modified solder joints obtained at 250°C, standard metallographic procedures were applied. Changes in the microstructure, the thickness of the inter‐metallic compounds (IMCs) and their chemical compositions were observed by means of scanning electron microscope (SEM) and energy dispersive spectroscopy (EDS).

As expected, a higher silver nanoparticle addition to the SAC solder paste resulted in better wetting properties on copper. The results indicated the possibility of an improvement of the reflow soldering process by using SAC solder paste with silver nanoparticles and by lowering its soldering temperature. An improvement was also observed in the wettability with a decrease in the silver nanoparticle grain size. Also, the wettability proceeded at a lower temperature (20°C lower) than that for the SAC paste, without the nano‐additives. For the 4 per cent silver nanoparticle addition, Ag₃Sn star‐like IMCs were also found, which grew with the lowering of the silver nanoparticle grain size.

Further studies are necessary for confirmation of the practical application, especially of the mechanical properties, as well as the reliability properties of the solder joints, for the chosen solder paste with silver nanoparticles.

Taking into account the wetting data, the best results of the “nano” SAC solder pastes were obtained for the highest addition of the silver nanoparticles. It was found that the spreading on copper was higher and the contact angles were lower for the SAC solder paste with 4 per cent (by wt.) of 138‐nm grain size silver nanoparticles. A comparison of SAC solder pastes with a 4 per cent silver nanoparticle addition but of a different grain size (138‐9 nm), suggested a further improvement in wetting properties with lowering of the silver nanoparticle grain size. The results suggested the possibility of an improvement in the reflow soldering process by using SAC solder paste with silver nanoparticles and by lowering its soldering temperature.

Spreading, wetting and contact angle measurement methods were used for the wetting determination of the SAC solder paste with the silver nanoparticles on copper under the same temperature conditions. Also, the microstructure of the solder joints obtained at 250°C was determined with the use of SEM and EDS methods. The results obtained made it possible to draw conclusions regarding the correlation between the output of the wetting results and the amount and the grain size of the added silver nanoparticles, and also the microstructure and thickness of the IMCs of the “nano” solder joints.

The concept of utility was the first time applied in Economics. The purpose of this paper is to report its usefulness for the decision making in complex technological systems, in general and in computer networks, in particular. Three selected decision-making problems are considered, corresponding solution algorithms are explained and results of numerical experiments are presented for the selected real-world case study.

Referring to similar decision-making problems in Economics, three problems of different time horizon are investigated: strategic investment planning, short-term network rate allocation and on-line network operating. Deterministic and uncertain versions are taken into account, and the latter one is handled more thoroughly. The formalism of uncertain variables is used to represent the parameter uncertainty which concerns users’ demands for services in computer networks as well as network links’ capacities. Corresponding optimization tasks are presented. Numerical experiments concerning a part of the computer network Pionier working in Poland confirmed the usefulness of the solution algorithms proposed.

The carried out numerical experiments verified the importance and worth of the decision-making algorithms for the Pionier computer network. It particularly concerns the game theory-based algorithm solving the on-line network operating problem which enables calculating the rates for computer links distinctly, i.e., separately for every link.

More case studies should be considered to formulate more general corollaries. The application of utility concept for wireless sensor networks needs further studies on solution algorithms.

The results can be directly applied to a class of modern computer networks, e.g., content delivery networks, self-managing networks, context aware networks, multilevel virtual networks.

The paper presents the unified and systematic approach for individual results previously obtained, and it considers one case study.

This paper aims to investigate the effect of different beam distance by understanding laser beam influence on solder joint quality. The utilisation numerical-based simulations and experimental validation will help to minimise the formation of micro void in PTH that can lead to cracks and defects on passive devices.

The research uses a combination approach of numerical-based simulation using Finite Volume Method (FVM) and experimental validation to explore the impact of different laser beam distances on solder joint quality in PTH assemblies. The study visualises solder flow and identifies the optimal beam distance for placing a soldering workpiece and a suitable tolerance distance for inserting the solder wire.

The simulation results show the formation of micro void that occurs in PTH region with low volume fraction and unbalance heat concentration profile observed. The experimental results indicate that the focus point of the laser beam at a 99.0 mm distance yields the smallest beam size. Simulation visualisation demonstrates that the laser beam’s converging area at +4.6 mm from the focus point which provides optimal tolerance distances for placing the solder wire. The high-power laser diode exhibits maximum tolerance distance at 103.6 mm from the focus point where suitable beam distance for positioning of the soldering workpiece with 50% laser power. The simulation results align with the IPC-A-610 standard, ensuring optimal filling height, fillet shape with a 90° contact angle and defect-free.

This research provides implications for the industry by demonstrating the capability of the simulation approach to produce high-quality solder joints. The parameters, such as beam distance and power levels, offer practical guidelines for improving laser soldering processes in the manufacturing industry.

This study contributes to the field by combining high-power laser diode technology with numerical-based simulations to optimise the beam distance parameters for minimising micro void formation in the PTH region.