Introduction

Tin is a ubiquitous metal that is unlikely to become obsolete [1]. The remarkable properties of this metal have led to its applicability in a variety of scientific and industrial contexts within the last decade, including anode material for Li-ion [2], sodium-ion [3], lithium secondary [4], and all-vanadium redox flow [5] batteries, nanowires [6], and Pb-free alloy solders for use in semiconductor packaging [7], etc. Electrocatalyst for the electroreduction of CO2 to chemicals such as CO, formate, hydrocarbons, and methanol are of particular interest which in turn can lessen reliance on fossil fuels. This application can severely be preferred from environment and cost aspects [8]. Moreover, tin has conventional applications such as an alloying element in corrosion-resistant materials, surface coating for solderability improvement, food processing materials, soldering materials, printed circuit board, electronic and microelectronic products, etc. [9,10,11].

Electrodeposition is a dependable, accurate, and cost-effective method for preparing pure and tin alloy deposits [12, 13]. Industrial scale electrodeposition of tin was first employed more than six decades ago [14]. Electrodeposition processes ensure easy and precise controlling of the structure, thickness, and composition [12, 13] of metal deposits by either varying the deposition parameters or the chemistry of the electrolyte solution [15], resulting in (i) single-layer or multilayer deposits [12], (ii) materials with nanoscale compositional and structural differences [15], and (iii) porous layers [13, 15] on substrates of varying sizes and complex shapes [12].

Due to its high solubility and ease of deposition [16], a non-cyanide fluoroborate bath is one of the earliest baths to prepare tin and its alloys. Aside from the broad range of chemical compositions of tin alloys obtained from the fluoroborate bath, it is now used as a leaching acid in electrorefining technologies [17]. This is mainly due to its selective solubility of metals such as tin, lead, and copper [18, 19], especially in the case of valuable metals recovery from printed circuit boards and solder alloy by the hydrometallurgical process [19, 20].

Nucleation and growth mechanisms of electrodeposited materials are critical, particularly in nanostructured ones [15]. Many researchers have studied the electrodeposition process of tin from sulfate, chloride, and methanesulfonate baths and have calculated the kinetic parameters. They investigated the impact of temperature, concentration, additives, surfactants, etc. on tin electrodeposition process. However, despite the significance of the fluoroborate bath mentioned earlier, studies of its mechanisms seem to be subjected to oversight, and there have been limited researches on this topic.

In 1990, Lee et al. [21] obtained a cyclic voltammogram of tin from a fluoroborate bath on platinum, which revealed a diffusion peak of tin reduction at −0.65 V vs. SCE and an oxidation peak at around −0.1 V vs. SCE. Following this, Petersson et al. [22] in 2000 demonstrated that deposition of tin, lead, and tin–lead alloys from a fluoroborate bath onto a glassy carbon disc is a diffusion-controlled process with a three-dimensional growth mechanism; nucleation was instantaneous, the number of nucleation sites increased with potential, and the diffusion coefficient of tin was \(6.0\pm 0.2\times {10}^{-6} {\mathrm{cm}}^{2}{\mathrm{s}}^{-1}\). Afterward, Sun et al. [23] produced pure tin deposits with irregular dendritic morphology using a fluoroborate bath on a platinum substrate in 2004. Later on, Müller et al. [24] prepared deposits of diverse forms by electrodepositing tin from a fluoroborate bath onto boron-doped diamond substrates at various ion concentrations and deposition potentials. Finally, in 2013, Huang et al. [25] investigated the mechanism of tin nucleation and growth on a double reduction steel substrate from a N2 gas deaerated fluoroborate bath containing an antioxidant and a brightener. They demonstrated that this process is diffusion-controlled with 3D nucleation and subsequent grain growth. They also determined the number of active sites, nucleation rate constant, and proton reduction kinetics constant on the tin surface.

As mentioned earlier, mechanistic investigations of tin fluoroborate baths are few, and no research on graphite substrates has been conducted so far. In addition to the prominent advantages of graphite such as being user- and environment-friendly, affordable, and accessible [26]; high electrochemical reactivity, good mechanical rigidity [27], high chemical and mechanical stability; and a broad working potential window, the pencil graphite electrode (PGE) in turn offers some characteristics, that has extended its usage as an electrode in electrochemical cells in mechanistic investigations. A key feature is mass production as well as excellent control over the manufacturing process, which ensures a chemical composition homogeneity and uniform external surface quality [26]. Therefore, this study investigates the mechanism of tin reduction from a non-complex fluoroborate bath (without any additives and gas injection) onto PGE. First, the charge transfer and diffusion of cations to the working electrode surface were explored to acquire the reduction process restrictor. Then, the kinetic parameters of tin reduction and the HER were calculated. Finally, the morphologies of the resulting deposits were examined.

Experimental

Materials and Method

All the experiments have been conducted in a standard three-electrode electrochemical cell with a volume of 100 cm3 at room temperature (∼ 25 °C), with no agitation. The working electrode was a 0.5-mm-diameter graphite pencil rod, a typical substrate for investigating the nucleation and growth process [27]. A 1-cm2 platinum plate and a 3-molar-KCl Ag/AgCl electrode were employed as counter and reference electrodes, respectively. The reference electrode was placed in a Luggin capillary, and its tip was kept about 2 mm away from the working electrode surface to minimize IR drop errors. The distance between the working and counter electrode was also 2 cm in all experiments. The potentials reported in this article are relative to the Ag/AgCl reference electrode, which has a potential of +205 mV versus SHE. Before starting the experiments, the PGE was immersed in 0.5 M HNO3 to remove surface drosses, and all three electrodes were rinsed with distilled water before being inserted into the cell chamber.

Keeping in mind the capability of fluoroboric acid in the selective leaching of tin, tin oxide (instead of tin salt) was used as the source of tin in this study. Fluoroboric acid is vulnerable to dissolution into HF and free fluoride, causing tin to retain in solution in the form of the Sn(IV)hexafluorostannate ions. As such, H3BO3 is used to react with HF and reproduce the fluoroboric acid and increase electrolyte stability [28]. Table 1 shows the prepared electrolyte conditions.

Table 1 Chemical composition of the electrolyte (g/L)
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To determine the type of tin reduction and oxidation process, the cyclic voltammetry method was employed, and voltammograms at different scanning rates over the range of 4–100 mV/s were obtained. To obtain current transients by chronoamperometry technique, open circuit potential (OCP) (540 mV) was applied for a time of 60 s, followed by a 10-s constant cathodic potential step, ranging from −500 to −700 mV. The resulting data were used to calculate the kinetic parameters, including the diffusion coefficient, charge transfer coefficient, kinetic constant of tin cations reduction, number of active sites on PGE for tin cations reduction, nucleation rate constants, and the proton reduction kinetics constant on the tin and PGE surface.

Instruments and Software

All experiments were performed using an Autolab® model PGSTAT 302 N connected to a computer running Nova 1.6 software. Demo version of the KaleidaGraph software was used to fit the experimental data to theoretical models, and the kinetic parameters were calculated using fitting results. Conductivity of solutions was measured with a conductivity/TDS meter (Jenway model 4510).

Results and Discussion

Cyclic Voltammetry

Table 1 shows the concentrations of fluoroboric acid in two solutions used for this part. The first effect of increasing acid concentration was on bath conductivity, which rose from 54 to 190 mS/cm as the ion concentration in the bath increased [29]. The next effect was on the tin cations reduction mechanism, which can be derived from the cyclic voltammograms in Fig. 1. In these voltammograms, potential sweeping began from OCP (500 and 540 mV for PGE in solutions 1 and 2, respectively) and proceeded toward more negative values to conduct the reduction process first.

Fig. 1
figure 1

CV for electrodeposition of tin(II) cations with the scanning rate of 100 mV/s from a solution 1, b solution 2

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In Fig. 1a, which corresponds to the solution with a low concentration of fluoroboric acid, the current density of the forward branch decreases slightly at approximately −100 mV which may be due to the adsorption of Sn(IV) on the PGE surface. Depending on the type of stabilizer system, a given amount of Sn(IV) can be present in the solution [30]. Moreover, a small peak (a) appears before the main reduction peak (b), which may be due to the conversion of Sn(IV) to Sn(II) [31, 32]. In order to minimize the presence of Sn(IV) and unwanted subsequent reaction, the solution must contain a sufficient amount of fluoride ions [30]. Accordingly, the initial cathodic current and peak (a) are eliminated at higher concentrations of fluoroboric acid, as seen in Fig. 1b. The broadness of peak (d) might be due to the remaining some Sn(IV) in the solution and making electrochemical reaction kinetics more complicated [28]. Despite this, by considering that single reduction peak is appeared in cyclic voltammogram and that most of the tin cations in the bath are in divalent form with increasing fluoroboric acid concentration, the general reduction reaction can be considered as follows:

$${Sn}^{2+}+2e\to Sn$$
(1)

As a result of the preceding, solution 1 was eliminated, and the rest of the experiments were conducted in the bath containing a high fluoroboric acid concentration (solution 2).

According to Fig. 1b, the reduction of tin cations starts at about −460 mV and peaks at −560 mV. Then the cathodic current reduces due to the depletion of tin cations at the interphase and the diffusion phenomenon. The appearance of such peaks in voltammograms suggests diffusion-controlled nucleation and growth process [33]. At potentials less than −800 mV, the amount of cathodic current density increases suddenly due to the hydrogen evolution reaction (HER). After that, the potential sweeping direction reversed at −1000 mV, and the reverse and forward branches had a crossover, indicating nucleation and growth of a new phase on the working electrode surface [2, 34]. Over the potential range of −485 < E <  −400 mV, the cathodic current density of the reverse branch is greater than that of the forward branch, indicating that tin nuclei grow faster and easier on tin substrate rather than graphite substrate [35].

The peak (e) at −270 mV is related to tin oxidation and suggests the dissolution of reduced tin in the cathodic branch. The single sharp peak (e) denotes a one-step reaction as follows:

$$Sn\to {Sn}^{2+}+2e$$
(2)

At the end of the cycle, the current reaches zero, indicating the complete dissolution of tin deposits and the lack of a passive tin layer. Furthermore, along with the fact that there was no deposit visible to the naked eye on the electrode surface after the test, the consistent OCP value before and after CV also suggests that the PGE surface has not changed.

Figure 2 shows the voltammograms in the smaller potential window and with different scanning rates. According to this figure, as the potential scanning rate increases, the current density rises and cathodic peaks shift toward more negative potentials. In addition, tin electrodeposition can be assumed to be an irreversible reaction due to the large distance between the anodic and cathodic peaks (greater than \(\frac{59}{n}\mathrm{mV}\) [36]; n = 2). For irreversible, diffusion-controlled processes, the Randles–Sevcik equation is as follows:

$${i}_{P}=\left(2.99\times {10}^{5}\right){n\left(\alpha {n}_{\alpha }\right)}^{1/2}{D}^{1/2} \,{C}_{O}^{\infty }{\nu }^{1/2}$$
(3)

where \({i}_{P}\), n, α, \({n}_{\alpha }\), \({C}_{O}^{\infty }\), \(D\), and ν are the current density of the cathodic peak, number of exchanged electrons involved in the electrode process, charge transfer coefficient of tin ions, number of electrons in the rate-determining step, the solution bulk concentration, diffusion coefficient, and the potential scanning rate, respectively [37]. According to this equation, the current density of the cathodic peak in irreversible diffusion-controlled processes is proportional to the square root of the scanning rate. Therefore, Fig. 3a, which shows the linear dependency of \({i}_{P}\) on \({\nu }^{1/2}\), confirms the irreversibility of the reduction process in this study. If the other parameters in Eq. (3) are known, the tin diffusion coefficient could be calculated by the slop of the straight line in Fig. 3a. According to Eq. (1), the values of n and \({n}_{\alpha }\) are equal to 2, hence the only unknown parameter in this equation is α. To determine α, the Gokhshtein equation can be used, which is as follows:

$${i}_{p}=-0.227 \,n\,F{C}_{O}^{\infty }{k}^{^\circ } \,exp\left(\frac{-\alpha {n}_{\alpha }F}{RT}\left({E}_{P}-{E}^{^\circ \prime}\right)\right)$$
(4)

where \(F\), \(k^\circ\), \(R\), \(T\), \({E}_{P}\), and \({{E}^{0}}^{^{\prime}}\) are the Faraday constant, the kinetic constant of tin ions reduction, the universal gas constant, temperature, the peak potential, and formal potential, respectively [38, 39]. The following equation is obtained by taking the \(natural\) logarithm on both sides of the Gokhshtein equation:

Fig. 2
figure 2

CV for electrodeposition of tin(II) cations with different scanning rates

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Fig. 3
figure 3

Extracted graphs from cyclic voltammograms of fluoroborate bath for a Randles–Sevcik, b Gokhshtein equations

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$$\mathit{ln}\,{i}_{p}=\mathit{ln}\left(0.227 \,nF{C}_{O}^{\infty }\,{k}^{^\circ }\right)-\frac{\alpha {n}_{\alpha }F}{RT}\left({E}_{P}-E{^\circ }^{^{\prime}}\right)$$
(5)

Therefore, by plotting \({\mathrm{lni}}_{\mathrm{p}}\) against \({E}_{P}-{E}^{^\circ \prime}\) and fitting that linearly, the amounts of \(\alpha\) and \(k^\circ\) could be obtained from the slope and y-intercept, respectively. This diagram is shown in Fig. 3b and its linear dependency is another confirmation of the irreversibility of tin reduction in this study. However, the y-intercept of Fig. 3a is non-zero, which may be due to additional phenomena other than diffusion-controlled process [40,41,42] (e.g., Nucleation [43]), slow ion transport across the interface [29] or non-faradaic currents contributing [44]. In this study, the distance between the electrodes (non-faradic current for the resistance of the solution) [44] and/or nucleation [40, 43] may be the reason for such deviation.

Table 2 lists the parameters calculated from Fig. 3, using the Gokhshtein and the Randles–Sevcik equations. The kinetic constant of tin ions reduction is from the order of 10−3, indicating a rapid reduction of tin ions from fluoroborate bath on PGE. Comparison of the diffusion coefficient obtained in this study with the values reported in the literature, which are listed in Table 3, shows that the value of this parameter from fluoroborate baths (this study and Huang et al. [25] results) is greater than other types of baths.

Table 2 The kinetic parameters obtained from cyclic voltammograms
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Table 3 Different amounts of diffusion coefficients in literature
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Step Potential Experiments

The driving force in electrocrystallization is electrochemical supersaturation, which is proportional to the electrochemical overpotential [45]. Electrochemical overpotential can be provided by lowering the potential or increasing the activity of electrolyte relative to its equilibrium state [45]. Since the electrolyte condition of this study is constant, the driving force was provided using negative potentials. Moreover, by altering the applied potential, the growth process can be manipulated to produce deposits with different morphologies [24]. Accordingly, the current transients generated by the chronoamperometry, which is based on applying different overpotentials through different potential steps, is used for determining the nucleation and growth mechanisms.

Figure 4a shows current transients with potentials stepping from −500 mV (more cathodic potential than \({E}^{^\circ \prime}\)) to −700 mV (more cathodic potential than \({E}_{P}\)). The general shape of all the current transients is similar. Initially, the current density increases sharply and reaches \({I}_{\mathrm{max}}\) at \({t}_{\mathrm{max}}\), indicating nucleation and growth process, then decreases gradually due to diffusion phenomenon, which is consistent with the Cottrell equation [29]. Finally, it reaches an almost stable value. The lack of a sharp current drop in the initial milliseconds indicates the absence of liminal phenomena such as Langmuir adsorption [35], charging of the electrochemical double-layer [22], etc.

Fig. 4
figure 4

a Current tranisients of tin cations reduction at different potential steps, b dimensionless (i/imax)2 vs t/tmax curves for electrodeposition of tin

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The Scharifker-Hills model is used for the primary evaluation of the nucleation and growth mechanism according to the following equations:

$${{\left(\frac{I}{{I}_{max}}\right)}^{2}}_{inst}= \frac{1.9542}{{t}/t_{max}} {\left\{1-exp\left[-1.2564\left(\frac{t}{{t}_{max}}\right)\right]\right\}}^{2}$$
(6)
$${{\left(\frac{I}{{I}_{max}}\right)}^{2}}_{prog}= \frac{1.2254}{{t}/t_{max}} {\left\{1-exp\left[-2.3367{\left(\frac{t}{{t}_{max}}\right)}^{2}\right]\right\}}^{2}$$
(7)

where \({I}_{\mathrm{max}}\) and \({t}_{\mathrm{max}}\) are the current and time corresponding to the maximum in current transients, respectively [46]. Figure 4b represents the Scharifker-Hills dimensionless curves and the normalized experimental data. Although the experimental data are closer to the instantaneous nucleation model, there is a slight positive deviation, indicating that the current consumed in the experiment was greater than the current required for instantaneous nucleation. This could be due to side reactions [25, 42, 47, 48], particularly HER in this study, which will be discussed in more detail below. In certain reduction processes, side reactions that are parallel to the main reactions consume some current. Accordingly, the current transient is the sum of the currents of all the reactions involved in the process. According to the Palomar–Pardavé model, the partial current density for diffusion-controlled three-dimensional nucleation and growth process is as follows [49, 50]:

$$\begin{aligned}{i}_{3D-dc}^{Sn}&={P}_{1}{t}^{-1/2}\left\{1-exp\left[-{P}_{2}\left(t-\frac{1-exp\left(-{P}_{3}t\right)}{{P}_{3}}\right)\right]\right\}; \\&{P}_{1}=\frac{zf{D}^{1/2}{C}_{O}^{\infty }}{{\pi }^{1/2}}; \\&{P}_{2}=2\sqrt{2}{\pi }^{3/2}{N}_{0}{{C}_{O}^{\infty }}^{1/2}{V}_{m}^{1/2}D; {P}_{3}=A\end{aligned}$$
(8)

where \(zf\), \(D\), \({N}_{0}\), \({V}_{m}\), and \(A\) are the molar charge transferred during electrodeposition, diffusion coefficient, the number of active sites, the molar volume of the deposit, and the nucleation rate constant, respectively. Because of the abundant presence of hydrogen cations in acidic electrolytes, the chance of hydrogen evolution during the reduction is very high, especially at higher cathodic potentials. Accordingly, in this study, HER co-occurs in the tin reduction potential range, as observed by the generation of hydrogen bubbles at the cathode surface. The first step of HER, which is called proton reduction, is the adsorption of hydrogen cations on the surface as follows [49]:

$${H}_{interface }^{+}+{e}^{-}\to {H}_{adsorbed}$$
(9)

Proton reduction is possible on both graphite and deposited tin substrates. Since the surface of PGE is gradually covered with tin deposits, the amount of proton reduction on the graphite drops while it rises on the tin. The following equations are used to calculate the current density of proton reduction on tin and PGE surfaces, respectively.

$$\begin{aligned}&{i}_{PR}^{Sn}={P}_{4}^{Sn}\left(1-exp\left[-{P}_{2}\left(t-\frac{1-exp\left(-{P}_{3}t\right)}{{P}_{3}}\right)\right]\right); \\&{P}_{4}^{Sn}={z}_{PR}{k}_{PR}^{Sn}F{\left(\frac{2 {C}_{O}^{\infty } {V}_{m}}{\pi }\right)}^{1/2}\end{aligned}$$
(10)
$$\begin{aligned}&{i}_{PR}^{PGE}={P}_{4}^{PGE}exp\left[-{P}_{2}\left(t-\frac{1-exp\left(-{P}_{3}t\right)}{{P}_{3}}\right)\right]; \\&{P}_{4}^{PGE}={z}_{PR}{k}_{PR}^{PGE}F{\left(\frac{2 {C}_{O}^{\infty } {V}_{m}}{\pi }\right)}^{1/2}\end{aligned}$$
(11)

where \({P}_{2}\) and \({P}_{3}\) are the same constants as within the Eq. (8), \({P}_{4}^{Sn}\) and \({P}_{4}^{PGE}\) are constants, and \({z}_{PR}\), \({k}_{PR}^{Sn}\), and \({k}_{PR}^{PGE}\) are the hydrogen cation charge (which is equal to one), the proton reduction reaction rate constant on the tin and PGE surface, respectively. Since the reduction of tin and hydrogen coincides, the total current density is the sum of these three partial current densities and obeys the following equation:

$$\begin{aligned}&i={i}_{3D-dc}^{Sn}+ {i}_{PR}^{Sn}+{i}_{PR}^{PGE}=\left({P}_{1}{t}^{-1/2}+{P}_{4}^{Sn}\right)+\\&\left[{P}_{4}^{PGE}- \left({P}_{1}{t}^{-1/2}+{P}_{4}^{Sn}\right)\right] exp\left\{-{P}_{2}\left[t-\frac{1-exp\left(-{P}_{3}t\right)}{{P}_{3}}\right]\right\}\end{aligned}$$
(12)

All five constants in this equation were obtained by fitting the curves of Fig. 4a and Eq. (12) using a demo version of the KaleidaGraph software. Figure 5 shows the experimental current transients fitted with Eq. (12) at two potentials. The partial current densities of three-dimensional diffusion-controlled reduction processes of tin, and HER on both tin and PGE surfaces are also plotted separately in Fig. 5. The perfect correlation of the experimental data to the theoretical model indicates the accuracy of the model used in these experiments. To better investigate the overvoltage effect on the HER partial current densities, these diagrams are redrawn in Fig. 6. The partial current densities of hydrogen evolution on the tin surface (dashed lines) are very low and approximately constant for all overvoltages which indicate that tin is not a suitable substrate for hydrogen generation from fluoroborate solution. However, the internal graph, which magnifies the beginning section of the curves, indicates that the initial slopes have grown slightly with overvoltage. Similarly, the slope of the initial part of the PGE curves (solid lines) becomes steeper with overvoltage and reaches zero quicker. The increased initial slope with overvoltage for both tin and PGE graphs and quick attainment of constant current for tin and zero current for graphite show that with increasing overvoltage, the surface of PGE is covered with tin deposits faster.

Fig. 5
figure 5

Experimental current transients fitted with the total and partial current equation at potential of a −550, b −700 mV vs. Ag/AgCl

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Fig. 6
figure 6

Comparison of partial current densities for HER on grown tin centers and PGE substrate at different potential steps

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The upper part of Table 4 shows the constants obtained through fitting the curves and kinetic parameters calculated using these constants. Based on these results, the diffusion coefficient is almost constant and independent of overvoltage. The average amount of diffusion coefficient obtained from the Palomar–Pardavé model is 0.96 × 10−5 cm2/s, which is consistent with the result of the Randles–Sevcik equation in the previous Sect. (1.35 × 10−5 cm2/s). The slight difference between these two values is due to the difference in the primary data, the equations and methods used in their calculation [51]. It is also clear that the nucleation rate constants and the number of active sites increase with overpotential. The amounts of nucleation rate constant obtained in this study (3.88–47.32 1/s) are consistent with the amounts reported by Huang et al. [25] (2.67–57.5 1/s), and the slight difference is due to the different applied overvoltages. Table 5 lists the number of active sites for the tin cations reduction in the literature with various baths and substrates. Comparing the amounts listed in Table 5 with each other and with the values obtained in this study reveals that the number of active nucleation sites obtained from other baths are often greater than that of fluoroborate baths. However, the amount of this parameter in this study (3.1–19.3 × 105 1/cm2) is greater than that reported by Huang et al. [25] (0.47–5.98 × 105 1/cm2), implying that the graphite has a more active surface for tin reduction than double reduction steel substrate.

Table 4 The kinetic parameters obtained from current transients
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Table 5 Different values of number of active sites for the reduction of tin cations and proton reduction kinetics constant on tin in literature
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To better compare the amounts of the proton reduction kinetics constant on the tin and PGE surface, listed in Table 4, these parameters are plotted in terms of potential in Fig. 7. According to this figure, the values of the proton reduction kinetics constant on the tin surface are very small compared to the values of this parameter on PGE. This is due to the low catalytic activity of tin metal for HER [52, 53]. This result corresponds to the partial current densities displayed for the HER on the tin according to the dashed curves in Fig. 6, which have low and approximately constant values for all overvoltages. The amounts of the proton reduction kinetics constant on the tin from different baths are also listed in Table 5. The value of this parameter in the fluoroborate bath is lower than that in other bath types, indicating the slow rate of proton reduction on tin in fluoroborate bath. However, the amounts of this parameter obtained in this study (3.8–5.4 × 10−7 mol/cm2 s) are larger than the amounts reported by Huang et al. [25] (0.11–1.56 × 10−7 mol/cm2 s), which might be due to the lower pH in this study (pH = 1). Contrary to tin, the amounts of proton reduction kinetics constant on the PGE surface are large and increase with overvoltage. This result corresponds to the increasing initial current density of the partial current densities shown by the solid line in Fig. 6, which indicates faster hydrogen gas generation on the PGE with an increase in overvoltage.

Fig. 7
figure 7

Relation between the proton reduction kinetics constant on grown tin centers and PGE substrate with deposition potential

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In order to show the accuracy of the abovementioned results, \(i-{t}^{1/2}\) and \(i-{t}^{3/2}\) diagrams for the initial part of current transients were plotted in Fig. 8. The good linear correlation of \(i-{t}^{1/2}\) proves the instantaneous nucleation. The number of active nucleation sites was calculated using Eq. (13) [46]. These values are also listed in Table 4.

Fig. 8
figure 8

Ascending parts of the current transient at different deposition potentials: a i-t1/2, b i-t3/2

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$$i=-5.012nF{D}^{3/2}{{C}_{O}^{\infty }}^{3/2}{V}_{m}^{1/2}{N}_{0}{(t-{t}_{0})}^{1/2}$$
(13)

Figure 9 shows the \(i-{t}^{-1/2}\) for the descending part of the current transients. The diffusion coefficient was calculated from the slope of this line using the Cottrell equation as follows [29]:

Fig. 9
figure 9

Cottrell analysis of descending parts of the current transient at different deposition potentials

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$$i=-0.564nF{C}_{O}^{\infty }{D}^{1/2}{t}^{-1/2}$$
(14)

The average value of the diffusion coefficient obtained from this graph (0.96 × 10−5 cm2/s) is entirely the same with the amount obtained from the Palomar–Pardavé et al. model (0.96 × 10−5 cm2/s).

Morphology

Figure 10 displays the SEM images of tin deposits resulting from 5 s of potentiostatic electrodeposition. Although the nuclei have spherical shapes in both potentials, dendriticization has begun in some parts, as highlighted in the figures. The substrate surface between the nuclei is visible at a potential of −500 V. However, as the overvoltage rises, the number of nuclei on the surface increases, resulting in better surface coverage. The nuclei deposited on graphite in this study are more uniform in size than those on the steel substrate [25] except for dendrite seeds.

Fig. 10
figure 10

Morphology of tin deposits resulting from cathodic potential of a −500, b −600 mV vs. Ag/AgCl for t = 5 s

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The amount of overvoltage or current applied to the cathode and the concentration of tin cations in the solution affect the morphology of tin deposits from the fluoroborate bath. Increasing the amount of these parameters leads to more complicated structures such as dendrites [24]. The concentration gradient at the tip of the dendrites, on the other hand, is steeper than at a flat surface when the process is diffusion-controlled. Therefore, diffusion is quicker at peaked parts, and the tip of the dendrites grows rapidly [54]. Figure 11 depicts the deposits grown for 20 s at potentials of −500, −600, and −800 mV. In all three potentials, dendritic structures are perfectly congruent with the morphology of the deposits created by Müller et al. at similar concentrations and high overvoltages [24]. According to Fig. 11a, at −500 mV, free-standing dendrite seeds are noticeable on the substrate surface, only with a few fern-like grown dendrites. However, on the one hand, according to Fig. 11b, more dendrites had formed with increasing overpotential. On the other hand, under potentiostatic circumstances, the creation of dendritic deposits increases the cathode surface, giving the cations additional sites to reduce [54]. Consequently, a tangled tin deposits layer is formed on the surface of the PGE, covering the surface of the substrate entirely, as shown in Fig. 11b. What is more, the dendrites obtained at −600 mV are shorter and less sharp when compared to those at −500 potential since the higher hydrogen generation rate at higher overvoltages and its stirring effect [25] prevent the depletion of the cathode interface from tin cations. This allows the reduction process to continue with a weaker diffusion limitation, which in turn lessens sharp dendrites [54]. Finally, at −800 mV, the potential at which the hydrogen generation is high, and the hydrogen release sites remain as cavities in the deposited layer. This phenomenon causes the dendrites to form a foam-like shape and generates an extremely low-density deposit layer. It should be noted that again for the same reason stated for the −600 mV, the dendritic teeth on a stem have grown to lower extent than that of −500 mV, but they are closer to each other and have created a continuous structure (internal image in Fig. 11c).

Fig. 11
figure 11

Morphology of tin deposits resulting from cathodic potential of a −500, b −600, c –800 mV vs. Ag/AgCl for t = 20 s

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Conclusions

Here, electrodeposition of tin cations was performed from a fluoroborate bath on PGE at room temperature. First cyclic voltammetry and chronoamperometry techniques were established to investigate the kinetics and electrochemical nucleation/growth mechanisms of tin reduction. Then SEM analysis was used to examine the morphology of the tin deposits. Two peaks appeared in cyclic voltammograms; (i) one in the forward branch indicating the diffusion-controlled reduction of tin cations, and (ii) another in the reverse branch for dissolution of reduced tin. In addition, investigating the data obtained from the voltammograms at different potential scanning rates, using Randles–Sevcik and Gokhshtein equations, revealed that the reduction of Sn(II) to Sn is an irreversible process, and the diffusion coefficients, the charge transfer coefficient, and the kinetic constant of tin cations reduction were found to be 1.35 × 10−5 cm2/s, 0.28, and 1.94 × 10−3 cm/s, respectively.

Analyzing current transients obtained from chronoamperometry by Sharifker-Hills and Palomar–Pardavé et al. models revealed that the nucleation process of tin over PGE is instantaneous, followed by 3D diffusion-controlled growth mechanism accompanied by the hydrogen reduction reaction. Furthermore, the fitting results showed that the number of active nucleation sites, the tin nucleation rate constant on PGE, and the proton reduction rate constant on the PGE increase with overvoltage. Moreover, the proton reduction rate constant on the tin surface was low and less than that on the PGE surface indicating low catalytic activity of tin metal for proton reduction. The diffusion coefficient of tin species was derived using the Cottrell equation and Palomar–Pardavé et al. model, which agreed with CV measurements.

The morphological study using SEM showed that initial nuclei formed from fluoroborate on PGE have uniform spherical shapes, but grew dendiritically which is compatible with diffusion-controlled conditions. The dendrites became finer, interconnected, and interwoven with the increase of overvoltage, but due to the intense formation of hydrogen gas at higher overvoltage and the remaining release sites as cavities in the deposited layer, a non-dense and foam-shaped structure was obtained.