Integrated Platform for Determining Solderability Parameters: Module for Measuring the Surface Tension of Liquid Solders

Abstract

This article describes a module and method for measuring the surface tension of liquid solders implemented on a measuring device as part of an integrated platform for automatic measurement of brazebility parameters at high temperatures. A concept for constructing a test stand is presented, with a description of the individual functional blocks. The developed stand allows for testing of the solder’s surface tension. The surface tension is one of the parameters that describe the thermodynamics of interfacial reactions and the structure of newly created joints. Determining the physicochemical interactions between liquid and solid substances is crucial for various industrial processes in fields such as metallurgy, electronics, and aviation, mainly where soldering and brazing technologies are employed. A series of bubble experiments in solder for a ceramic capillary is carried out to verify the proposed method using the developed system. One of these experiments is described in this article.

1. Introduction

The dynamics of the wetting process of bonded surfaces is a technological element that affects the selection of materials and solders as well as the choice of process parameters such as temperature, time, protective atmosphere, and fluxes. The liquid solder’s surface tension decisively influences the dynamics of the wetting process [1]. Therefore, it is necessary to know the surface tension value in order to determine the technological parameters of the soldering process, which are determined by the lift height and solder gap filling time [2,3]. The integrated platform enables the determination of the wetting braze parameters (the wetting force based on the immersion experiment method and surface tension based on the immersion and maximum gas bubble experiment methods) [4]. The surface tension is one of the parameters that describe the thermodynamics of interfacial reactions and the structure of newly created joints [5]. The surface tension is the consequence of the unbalanced attraction forces acting on the particles located on the fluid surface, causing the fluid to decrease its surface area [6]. As the outcome of the surface tension, the fluid forms the shape with the minimum surface area with respect to the volume factor [7]. The surface tension parameter plays a vital role in many industrial metallurgical processes, which is contributed to by the field phase [8]. Nowadays, measurement of the surface tension is possible using many techniques, which can be classified into one of the following groups: direct microbalance measurement (Wilhelmy plate, Du Nouya ring), capillary pressure measurement (maximum bubble pressure, growing drop), analysis of capillary–gravity forces (capillary rise, drop volume), gravity-distorted drops (pendant drop, sessile drop), and reinforced distortion of the drop (spinning drop, micropipette) [9,10]. The complexity and suitability of these techniques for different groups of materials (viscous liquids, melted metals) and the accuracy of their results differ [11,12]. In the next chapter, the method implemented in the measurement system is presented.

2. Maximum Bubble Pressure Method

This method consists of slowly blowing bubbles of inert gas into the tested liquid using a tube, the outlet of which is located under the surface of the liquid. The process of forming the gas bubbles is presented in Figure 1. The A–B stage (Figure 1) corresponds to the rise in pressure related to the bubble forming. The shape of the gas bubble’s surface and the registered pressure value depend on the capillary wetting by the fluid metal. The maximum pressure $Pmax$ appears at point C (Figure 1), where a bubble with a semisphere shape and a radius equal to the capillary radius is assumed. Between the D and E points (Figure 1), the radius of the bubble curvature increases while the pressure drops. At point E (Figure 1), the gas bubble is released from the capillary [13,14].

In the case of a small-diameter capillary, the bubble retains the shape of a part of the sphere’s surface during enlargement, with the size of its radius passing through the minimum when the bubble becomes a hemisphere. The radius of the bubble is then equal to the radius of the tube; as the size of the bubble then reaches its minimum $\mathsf{\Delta }P$, it reaches its maximum size at this point. Therefore value $\mathsf{\Delta }{P}_{max}$ is provided by Equation (1), in which r is equal to the radius of the tube and $\sigma$ is equal to the surface tension of the liquid. When a liquid wets the tube material, a bubble forms on the inner wall of the tube, with r being the inner radius of the tube. The maximum pressure is determined experimentally in the tube, where the bubbles lose their ability to grow further and break off. In addition, it should be considered that the tube outlet is located at a certain assumed distance from the surface of the liquid h. Therefore, $\mathsf{\Delta }{P}_{max}$ equals $(P_{max}-P_h)$, where $P_{max}$ is the maximum pressure being measured and $P_h$ is the hydrostatic pressure of the liquid column with a height h [11,14].

$$\mathsf{\Delta }P=2\sigma /r$$

(1)

2.1. Analysis of Surface Tension Using the Maximum Bubble Pressure Method

The method of measuring the surface tension of solders at high temperatures consists of measuring the changes in the pressure of the gas supplied to the capillary immersed in liquid metal to a specified depth h. The experiment is carried out at high temperatures with protective gases. The experiment begins the initial process of stabilising the thermodynamic conditions in the furnace chamber. At this stage, the chamber is heated in the presence of a gaseous protective atmosphere [14]. The actual measurement experiment begins with the immersion of the capillary in liquid solder to a preset depth h. During the experiment, the pressure inside the gas bubble is recorded under a pressure-controlled gas supply outside. Between points A and B in Figure 2, there is an increase in gas pressure corresponding to bubble formation. The shape of the gas bubble surface and the value of the recorded pressure depend on the wettability of the capillary material by the liquid metal. At point C, there is a maximum pressure $P_{max}$, and it is assumed that at the same time the bubble has the shape of a hemisphere with a radius equaling that of the capillary. Between D and E, a decrease in pressure inside the capillary is observed while the radius of curvature of the bubble is increasing. Point E corresponds to the detachment of the follicle from the capillary [11]. At equilibrium, the pressure in the bubble $P_p$ balances the sum of pressures limiting the increase in the bubble’s volume.

For each point A of the bubble surface, the following occurs (2):

$$P_p=P_r+P_h\left(A\right)+P_{\sigma }\left(A\right),$$

(2)

where:

• $P_p$—Pressure in the bubble (for practical purposes, this does not depend on point A).
• $P_r$—Pressure in the retort above the bath surface (does not depend on point A).
• $P_h\left(A\right)$—Hydrostatic pressure (a function of the depth h relative to the bath surface).

In the experiment, the differential pressure is measured; the relation (2) can be simplified (3):

$$\mathsf{\Delta }P=P_h\left(A\right)+P_{\sigma }\left(A\right).$$

(3)

The $P_h\left(A\right)$ value is expressed by Equation (4):

$$P_h\left(A\right)=\rho gh\left(A\right),$$

(4)

where:

• $\rho$—Density of the bath material.
• g—Acceleration due to gravity.
• $h\left(A\right)$—Depth of immersion of point A in the bath.

The value of $P_{\sigma }\left(A\right)$ depends on the surface tension of $\sigma$ and the local curvature of the surface at point A. In the general case, this is expressed by the relation (5):

$$P_{\sigma }=\sigma ({\displaystyle \frac{1}{R_{1A}}}+{\displaystyle \frac{1}{R_{2A}}})$$

(5)

where $R_{1A}$ and $R_{2A}$ are the radii of curvature at point A on two orthogonal lines passing through point A. Thus, the relation (3) takes the following form (6):

$$\mathsf{\Delta }P=\rho gh\left(A\right)+\sigma ({\displaystyle \frac{1}{R_{1A}}}+{\displaystyle \frac{1}{R_{2A}}}).$$

(6)

In the case of a spherical surface, both radii of curvature are equal to each other and equal to the radius of the sphere R; thus, the following equation holds for the sphere (7):

$$P_{\sigma }={\displaystyle \frac{2\sigma }{R=const}}.$$

(7)

From Equation (6), it follows that the bubble does not have the shape of a spherical bowl, as the value of $P_h$ increases at a constant value of $\mathsf{\Delta }P$ with the depth of immersion of point A; thus, the value of the second component of the sum must decrease, leading to the conclusion that the deeper the local radii of curvature, the larger the bubble. The bubble is somewhat flattened, and takes on a shape similar to a rotary ellipsoid; this is identical to the lying droplet method, where hydrostatic pressure pushes the droplet to the sides and into a flattened hemisphere [11,13,15]. However, the bubble method of measuring surface tension assumes that at a particular stage of the experiment, when the pressure reaches its maximum value near the edge of the capillary, the shape of the bubble surface differs only slightly from the spherical surface of radius r; for this moment of measurement, Formula (6) takes the form (8)

$$\mathsf{\Delta }P=\rho gh+{\displaystyle \frac{2\sigma }{r}},$$

(8)

where:

• h—Capillary immersion depth.
• r—Capillary radius.

With this assumption, the value of $\sigma$ can be calculated from Equation (9):

$$\sigma =(\mathsf{\Delta }{P}_{max}-\rho gh){\displaystyle \frac{r}{2}}.$$

(9)

2.2. Introduction of Measurement Correction

A closer analysis of the problem shows that the above assumption (for $P_{max}$, the bubble has a hemispheric shape with radius r) introduces a specific error of method, which is the more significant as the value of the quotient $\rho /\sigma$ becomes higher. The more critical its value, the more flattened the hemisphere is, taking on a shape like a rotational ellipsoid [14,15]. Under these conditions, the maximum pressure occurs in a bubble with a larger volume than that of a hemisphere with radius r. Mathematical analysis of the dependence of the bubble geometry on the value of this quotient allowed the formula for the correction of the surface tension value to be derived as follows (10):

$${\sigma }_k={\displaystyle \frac{r\mathsf{\Delta }{P}_{max}}{2}}[1-{\displaystyle \frac{2}{3}}g{r}^{2}w]$$

(10)

where:

• $w=\rho /\sigma$—The value of surface tension determined from (9).
• ${\sigma }_k$—The adjusted value.

Schrodinger formulated a modified version of Equation (9), which was used for the studied systems (11) [11,15].

$${\sigma }_k={\displaystyle \frac{r\mathsf{\Delta }{P}_{max}}{2}}[1-{\displaystyle \frac{2}{3}}g{r}^{2}w-{\displaystyle \frac{{\left(r^{2}gw\right)}^2}{12}}].$$

(11)

The diagram below (Figure 3) shows examples of the values of the correction factor $ϵ=\sigma /{\sigma }_k$ as a function of the quotient $\rho /\sigma$ calculated from the relationships in (9) (the red waveform in Figure 3) and (10) (the blue waveform in Figure 3) for a capillary with a radius of $r=1$ [mm]. As can be seen, for the value of $\rho /\sigma <2·{10}^4$ there is complete agreement of the correction calculated using Formulas (9) and (10), while significant differences appear for $\rho /\sigma >3·{10}^4$. It should be emphasised that the smaller the mentioned error of the method, the smaller the radius of the capillary r.

3. Construction Concept and Construction of the Measuring Platform

The main requirement for an integrated platform for automatic measurement of wetting and surface tension is that it enable measurement experiments to be conducted at high temperatures in an automatic, repeatable, and human-independent manner according to a defined pattern that specifies the basic parameters of the technological process. Implementing such a task requires constructing a system that supervises the operation of individual executive and measurement systems during the experiment based on elements of automation and mechanics. Figure 4 shows the design assumptions of the main components of the experimental stand. The main component is the heating system, shown in Figure 4 point A (1—airlock, 2—furnace casing, 3—upper protection plate, 4—retort flange, 5—furnace mounting rear wall). Figure 4 point B shows the heating system furnace retort concept (1—crucible with bath, 2—crucible base, 3—thermocouple, 4—loading system base, 5—heating element). Figure 4 point C shows the running gear, including the concept of a precise mechanism for controlling the movement of the stage (1—stepper motor, 2—transmission system, 3—ball screw, 4—guide shafts, 5—rolling bearings) [4].

Figure 5 shows an overview of the experimental stand in the measuring laboratory (1—furnace system, 2—loading system, 3—furnace retort lock).

The architecture of the integrated platform for automatic measurement of wettability and surface tension consists of functional blocks that perform separate tasks. The basic systems, consisting of heating, gas, weighing, and driving, are specified and supervised by a central control system implemented on a WAGO industrial computer equipped with additional expansion cards for communication (Figure 6). An additional component is an IT chip, which enables communication with an autonomous device [4].

3.1. IT System Architecture

The integrated platform for automatic measurement of wettability and surface tension of solders in the temperature range up to 1000 °C using various types of technological atmospheres is based on a distributed architecture.The IT system consists of the following components: a control subsystem, a management and visualisation subsystem, and a database subsystem (Figure 7) [4].

Each of the above-mentioned components is a solution in the hardware and software layers. The control subsystem consists of control and measurement components managed by a WAGO industrial computer equipped with communication expansion cards. The primary task of the subsystem mentioned above is to control the operation of individual components and their operation according to the set parameters of the experiment. The management and visualisation subsystem is a hardware and software configuration with middleware for data exchange between the control and database subsystems and a graphical user interface for interaction with the device operator. Both the database subsystem and the management and visualisation subsystem can be run on separate workstations if necessary. Individual subsystems communicate using a transmission channel provided by the appropriate IT infrastructure based on the TCP/IP protocol stack. In the case of distributed architectures, ensuring proper communication and data flow between individual components is crucial. The organisation of the transmission channel based on the TCP/IP standard enables the encapsulation of application layer protocols, i.e., Modbus TCP or SOAP, in the structures of computer networks. This ensures easy integration with the LAN networks of the target installation sites. The software has been divided into concurrent tasks, which differ in their expected startup period and execution priority. The division of tasks is shown in the activity diagram in Figure 8 [4].

The critical program that the PLC executes is the experiment sequence. It is responsible for the device’s operation scenarios, and supervises all other programs. The program model of the sequence is shown in the scheme in Figure 9.

Due to the dispersed nature of the IT system and the diversity of cooperating systems, it was decided to build a middleware based on Web Service technology. This solution is independent of the hardware platform and implementation, and provides specific functionalities using the SOAP and HTTP protocols. The middleware bridges the control and database subsystems and the visualization software. This forces it to be divided into implementing logic related to data manipulation in the database and a part responsible for communication with the automation system. The task of the middleware for communication with the database is to enable the downloading and editing of data archived in the database system and make them available using an appropriate visualization application. The task of the middleware for communication with the control subsystem is to enable the collection of the current status of devices and readings of the controlled quantities as well as the setting of parameters according to which the automated experiment of wettability or surface tension measurement will be carried out. The visualization software offers the end user a graphical representation of the current status of individual components of the device and the course of the experiment. I addition, it allows for the viewing and analysis of previously performed experiments and the editing of database data. The assumptions made regarding the functioning of the measuring station and conducting experiments result in the stored data having a specific structure. The measurement experiment is carried out according to preset rules (template) specifying the parameters of the process, serving to control its condition by the automation system. The experiment template also contains information about the solder material and the samples (material, type, and geometry) on which the experiment is performed. Knowledge of this information is necessary for reporting and analysis of the performed experiments. The experiments are registered in the system as entries binding the experiment date and the template according to which the experiment was conducted. The measurement results are recorded in a separate table [4].

3.2. Experimental Scheme

Experimentation requires the cooperation of all elements of the measurement system. While individual experiments differ in detail, the general outline of their course is similar. The sequence of actions performed by all system components, for example the bubble experiment, is presented in the following description. Measurement is carried out at high temperatures with protective gases. It is then necessary to start the heating chamber (Figure 10 point A), install a protective atmosphere (Figure 10 point F, E), and stabilise the parameters before starting the actual test (Initialization and Warmup). The furnace heating chamber is moved vertically using a stepper motor drive kit and a ball screw (Figure 10 point G) until the optical sensor (Figure 10 point D) detects the presence of a sample at its input (Figure 10 point C). When the sample is detected, the movement continues until the sample is placed inside the furnace retort at the preset position. It remains in the preset position to activate the sample’s surface for a certain period. In the next step, the vertical movement of the furnace towards the sample is continued until contact with the solder surface is detected. In the case of immersion experiments, contact is detected by detecting changes in sample weight in the weighing module. For bubble experiments, contact is detected by an electrical sensor. Contact between the electrodes and the solder surface causes the electrical circuit to close. When contact is detected, the sample is placed at a preset depth (trigger Sample immersion; see Figure 10 point B) and remains for a preset stabilisation time. The sample is then drawn above the solder, triggering Specimen Ascent Above Solder, and stays there for a set period. Finally, the sample emerges from the furnace chamber (inducing Sample Ascent), which ends the experiment [4].

3.3. Module for Measuring the Surface Tension of Liquid Solders: Construction

The integrated platform for automatic measurement of wettability and surface tension is equipped with three gas lines to control the flow of gases in a protective atmosphere, along with a reduction atmosphere and a bubble system. All gas lines are connected to MFC mass flow controllers calibrated for the respective gas (Figure 11, item 1). For the bubble installation, the MFC output is connected to an accumulation tank with a capacity of 50 cm³, in which a constant gas pressure is maintained (Figure 11, item 2). The solenoid closes the outlet of the accumulation tank (Figure 11, Item 3). Excess gas is vented using the bleed valve (Figure 11, Item 4), the output of which is led outside the appliance area. The tank feeds a dosing system built using an adjustable needle valve (Figure 11, item 5). The needle valve output is connected to the pressure sensor (Figure 11, item 6) and to the output for connecting the handle to the capillary (Figure 12) [4].

4. Results of the Experiment

A view of the finished station used for conducting experiments is shown in Figure 13.

The experimental parameters are presented in the

Table 1. The bubble experiment settings in solder (S-Sn97Cu3) for a ceramic capillary Al₂O₃.

Parameter	Value
Temperature	250 [°C]
Capillary material	Al2O3
Surface activation time	60 [s]
Sample immersion time	120 [s]
Sample Standstill Time After Experiment	30 [s]
Immersion depth	6 [mm]
Capillary diameter	3 [mm]
Crucible Filling	S-Sn97Cu3
Solder Density	7300 [kg/m3]

.

A ceramic capillary is used in the bubble experiment. The solenoid valve is opened after activating the capillary surface, and the gas mixture is pumped through the capillary. This is accompanied by a move towards the solder, where the capillary is placed at a preset depth after detecting contact with the solder surface. A part of the recorded course of pressure changes as a function of time for the bubble experiment is presented in Figure 14.

During the bubble stage, the maximum recorded pressure obtained was ${\mathrm{P}}_{max}$ = 11.83 [mbar] and the generation time of a single bubble was about 0.9 [s]. After the bubbling stage in the solder is completed, the capillary is pulled out above the solder mirror. The experimental results are presented in

Table 2. The bubble experiment results in solder (S-Sn97Cu3) for a ceramic capillary Al₂O₃.

Parameter	Value
Maximum Pressure	11.83 [mbar]
Surface tension $\sigma$	565.55 [mN/m]
Corrected surface tension ${\sigma }_k$	458.13 [mN/m]

. The surface tension value determined according to the relation in (9) is $\sigma$ = 565.55 [mN/m]; after considering the correction according to Formula (10), the surface tension is ${\sigma }_k$ = 458.13 [mN/m].

5. Discussion

Nowadays, the conditions for producing good-quality material joints are determined by equilibrium wettability tests and the value of surface tension. In this paper, a methodology for surface tension measurement, including a general concept of the immersion experiment and calculation of its parameters, is presented. The methodology was used in the construction of an automatic research stand containing an integrated platform for automatic determination of high-temperature braze wettability, enabling a comprehensive study of the dynamic properties of brazes at temperatures of up to 1000 °C with various technological gas atmospheres. The surface tension parameter plays an important role in many industrial engineering processes due to its contribution to the fluid phase, including the creation of joints based on brazing or soldering technologies. Knowledge of the surface tension and its dynamics as well as the materials’ physical and chemical properties allows for the design of new materials and joining technologies as well as the optimisation of the existing ones. Today, research in materials engineering also focuses on methods for automatic measurement of joining process properties, i.e., wetting force and surface tension, the quantitative description of which allows for easy comparison of the results. Example experiments for the solder material S-Sn97Cu3 are shown. The results are in line with the values known from the literature [16,17,18]. In summary, our work bridges theory and practice, advancing joining technologies and reliable material design. Our contributions lie in developing a robust measurement technique and its application to high-temperature brazing, enhancing the understanding of joint dynamics and enabling informed choice of materials.